How to answer prove questions is to establish that a statement must be true using a valid chain of logical reasoning. Strong proofs begin from accepted definitions, axioms, theorems or previously established results and connect each step until the required conclusion follows.
A proof is different from checking several examples. Examples can suggest a pattern, but a general mathematical claim requires reasoning that covers every case allowed by the statement.
This guide explains how to read a proof target, identify assumptions, choose a proof method, justify each step, avoid circular reasoning and check that the final argument establishes the exact statement asked.
This guide is written for students, parents and educators who want a practical answer to how to answer prove questions in mathematics exams. The aim is to turn the command word into a reliable exam routine that can be practised, checked and transferred to unfamiliar questions.
The 60-Second Answer
Write the statement and assumptions clearly. Decide whether direct proof, contradiction, contrapositive, induction, algebraic proof, geometric proof or another syllabus method fits. Begin from known facts, not from the unproved conclusion. Justify each transformation or implication. Cover all required cases. Finish by stating exactly why the target statement follows.
Working definition: A prove question asks the learner to confirm the truth of a given statement using a chain of logical mathematical reasoning.
Why Prove Questions Matters
Proof establishes necessity, not merely plausibility.
A few successful numerical examples cannot establish a universal mathematical statement.
Clear proof writing also reveals where assumptions, definitions and logical implications enter the argument.
Command words are not decorative verbs. They tell the learner what kind of intellectual work the examiner expects. A student can know the topic and still lose marks by performing the wrong operation.
The Hidden Problem: Examples Can Support a Conjecture Without Proving It
Students often test three or four values and become convinced a statement is true.
A single untested counterexample could still destroy the claim.
A proof must cover the full domain described by the statement, not a convenient sample.
The Operating Model
Decode Statement → List Assumptions → Choose Proof Method → Start From Known Facts → Build Logical Chain → Cover Cases → Conclude Exactly.
Each stage has a separate job. Interpretation identifies what must be produced. Selection chooses the relevant information or principle. Construction turns that into a markable answer. Checking verifies scope, precision and completeness. Retesting shows whether the skill transfers to a changed context.
How to answer prove questions: Step by Step
1. Read the statement precisely
Identify quantifiers, conditions, domain and conclusion.
Small wording changes can change the proof.
2. List assumptions and known results
Separate what is given from what must be proved.
Do not smuggle the conclusion into the premises.
3. Choose a proof method
Decide whether direct reasoning, contradiction, contrapositive, induction, cases, algebra or geometry fits.
Method choice should match structure.
4. Start from accepted facts
Use definitions, axioms, theorems or givens.
Avoid beginning with the unproved result unless working equivalently in a method where that is justified.
5. Justify each step
Every implication, equality or transformation should have a valid reason.
Do not rely on it is obvious when a step is substantial.
6. Cover all required cases
If the domain splits into cases, handle each or use a method that covers all.
One example is not enough.
7. Avoid circular reasoning
Do not use the statement being proved as a reason for itself.
Check dependency.
8. State the conclusion
End by explicitly connecting the chain to the required statement.
Make the proof complete.
What Strong Performance Looks Like
- The statement is read precisely.
- Assumptions are separated from the conclusion.
- The proof method fits.
- Known facts are valid.
- Every step is justified.
- All relevant cases are covered.
- Circular reasoning is absent.
- The final conclusion matches the target.
These are observable behaviours. They can be modelled, practised and retested. The learner does not need a special exam instinct; the learner needs a reliable sequence of decisions that becomes faster with repetition.
Common Failure Modes
1. Example checking
Several cases are tested and called proof.
Use general reasoning.
2. Assuming the conclusion
The target statement appears as a premise.
Begin from givens and known results.
3. Circular proof
A later step depends on what the proof is trying to establish.
Break the loop.
4. Unjustified leap
The proof skips a nontrivial implication.
Add the reason.
5. Wrong proof method
The chosen method creates unnecessary complexity or fails to cover cases.
Reconsider structure.
6. Case omission
One branch of the domain is ignored.
Check completeness.
7. Notation ambiguity
Variables or domains are not defined clearly.
State them.
8. Conclusion mismatch
The proof establishes a related fact but not the target.
Return to the exact statement.
How the Strategy Changes Across Subjects
Mathematics
Proof is central: use valid definitions, algebra, geometry, contradiction, induction or other syllabus methods as appropriate.
The disciplinary standard remains decisive. General command-word strategy can organize the response, but subject knowledge determines whether the content and reasoning are actually valid.
Physics
Formal proof is less common, but mathematical derivations and demonstrations may require logically valid chains under stated assumptions.
The disciplinary standard remains decisive. General command-word strategy can organize the response, but subject knowledge determines whether the content and reasoning are actually valid.
Computer science
Proof may appear in correctness, invariants, induction or algorithmic reasoning at advanced levels.
The disciplinary standard remains decisive. General command-word strategy can organize the response, but subject knowledge determines whether the content and reasoning are actually valid.
Logic and discrete mathematics
Quantifiers, implication, equivalence and proof method selection are especially important.
The disciplinary standard remains decisive. General command-word strategy can organize the response, but subject knowledge determines whether the content and reasoning are actually valid.
Primary School, Secondary School and Examination Years
Primary school
Formal proof is usually not required, but children can build precursor habits: give a reason, show a pattern and distinguish one example from always true.
Keep the routine short, concrete and visible. Adults can model it first, then reduce prompts once the child can perform the decision independently.
Secondary school
Students should learn the difference between examples, demonstrations and proofs, and practise writing reasons for every nontrivial step.
Secondary learners should increasingly own scope, evidence, method choice and checking because questions become more varied and time trade-offs more consequential.
Before major examinations
Use changed statements and proof methods so learners cannot memorize one solution pattern. Check whether the proof covers the full domain.
Near major exams, mix command words in the same practice set so the learner must first identify what kind of thinking is required.
A Focused 60-Minute Practice Session
- 10 minutes — parse five proof statements for givens, domain and target.
- 10 minutes — select proof methods.
- 20 minutes — write one complete proof with reasons.
- 10 minutes — audit for circularity and missing cases.
- 5 minutes — rewrite one unjustified step.
- 5 minutes — state the final conclusion precisely.
The exact timings can change. What matters is command identification, independent attempt, feedback, targeted repair and fresh retest.
Diagnostic Checklist
- Is the statement understood exactly?
- Are assumptions separate from the target?
- Is the proof method appropriate?
- Are starting facts valid?
- Is every step justified?
- Are all cases covered?
- Is circular reasoning absent?
- Does the conclusion establish the exact statement?
Use the checklist to identify the earliest decision that failed. A wrong final answer may have begun with command confusion, evidence selection or method choice long before the final line appeared.
Practice Laboratory
Practice 1: Example-versus-proof
Classify arguments as examples, evidence or genuine proofs.
Explain why.
Practice 2: Method selection
Match statements to direct proof, contradiction, contrapositive, induction or cases.
Justify the choice.
Practice 3: Circularity hunt
Find where a flawed proof assumes its conclusion.
Repair the dependency.
Practice 4: Missing-reason fill
Add reasons beside each equation or implication.
Flag unsupported steps.
Practice 5: Case completeness
Given a domain split, list all cases before proving.
Check none are omitted.
Practice 6: Counterexample test
Try to find a counterexample before proving a universal claim.
Use failure to refine understanding.
Practice 7: Conclusion alignment
Compare the proved statement with the original target.
Repair scope mismatches.
Practice 8: Proof compression
After writing a full proof, remove redundant lines while preserving every logical step.
Improve clarity without losing rigor.
Three Student Cases
Case 1: Maren tests examples
Maren verifies a statement for five values and writes therefore proved.
Her tutor asks whether a sixth value could behave differently.
She learns why general reasoning is required.
Case 2: Iona assumes the target
Iona starts by writing the equation she is supposed to prove and manipulates it.
She is required to label givens and target separately.
Her arguments become logically valid.
Case 3: Leonie skips reasons
Leonie knows the route but omits why transformations are allowed.
She adds brief reasons beside nontrivial steps.
Her proofs become readable and checkable.
How Parents Can Help Without Taking Over
Parents can support prove questions by asking the learner to explain the command and response plan instead of supplying the answer. Useful prompts include: “What does the command word ask you to produce?”, “What information is relevant?”, “What method fits?”, “What would make this incomplete?”, and “How will you check?”
Once the learner can perform the decision reliably, remove the prompt. The goal is independent exam control.
How Tutors Can Use a Three-Student Small Group
In a three-student tutorial, prove questions becomes visible because one learner can attempt, another can challenge whether the command has been satisfied, and the third can check against a rubric, source or mark scheme. Roles then rotate.
After discussion, each learner completes a fresh individual question so shared explanation becomes personal performance.
How to Measure Progress
- Example-as-proof errors decline.
- Proof-method choice improves.
- Circular reasoning decreases.
- Reasons appear more consistently.
- Case coverage improves.
- Notation becomes cleaner.
- Conclusions align better with targets.
- Novel proof questions become less intimidating.
Marks are the final indicator, but process improvements often appear first: faster command recognition, fewer irrelevant sentences, stronger selection, cleaner working and more reliable checking.
A Four-Week Implementation Plan
Week 1 — Separate evidence from proof
Use simple universal claims and counterexamples.
Build logical awareness.
Week 2 — Practise proof methods
Use direct proof, contradiction and cases at the appropriate syllabus level.
State assumptions.
Week 3 — Improve proof writing
Require reasons, notation clarity and complete conclusions.
Audit circularity.
Week 4 — Simulate
Complete proof questions under time and classify failures by statement reading, method, logic or completeness.
Retest changed versions.
Evidence and Responsible Use
Cambridge International Further Mathematics defines prove as confirming the truth of a given statement using a chain of logical mathematical reasoning. This distinguishes proof from example checking or unsupported assertion.
Command-word meanings can vary slightly by subject and examination board. Use official syllabus wording, teacher guidance and mark schemes as the final standard, while using this framework to build transferable reasoning habits.
- Cambridge International AS & A Level Further Mathematics 9231 syllabus
- Cornell: How to Tackle Exam Questions
- Princeton: Preparing for Exams
Frequently Asked Questions
Is checking examples a proof?
No. Examples can support a conjecture but do not establish a universal claim.
Can I start from what I need to prove?
Not as an unproved assumption. Some algebraic approaches may work through equivalent statements, but the logic must remain valid.
Which proof method should I choose?
Use the structure of the statement and the methods allowed in your syllabus.
Do I need to write reasons?
Yes for nontrivial logical or algebraic steps, especially where the reason is not obvious.
What is circular reasoning?
Using the conclusion, directly or indirectly, as a premise for proving itself.
What if there are several cases?
Cover all relevant cases or use a proof method that handles them together.
How do I check a proof?
Verify assumptions, each implication, case coverage and whether the final statement exactly matches the target.
How do I practise?
Read many proof statements, choose methods before writing and compare your logical chain with rigorous model solutions.
Helpful Reading on eduKateSingapore
- How to Read Exam Questions
- How to Answer State Questions
- How to Answer Inference Questions
- How to Check Your Work
- How to Answer Demonstrate Questions
- How to Answer Justify Questions
Proof Establishes Necessity, Not Familiarity
A few correct examples can suggest a pattern, but they cannot establish a general theorem.
Read the statement exactly. Separate givens from target. Choose the method. Build the logical chain. Cover every case. Then state precisely what has been proved.
Properly taught kids shine a bright light into the future.
Extended Diagnostic Workshops
Workshop 1: Read the statement precisely × Assuming the conclusion
Set up one fresh exam-style question in which the learner must practise read the statement precisely while watching specifically for assuming the conclusion. Identify quantifiers, conditions, domain and conclusion. Require an independent response before any model is shown so the actual decision becomes visible.
The target statement appears as a premise. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 2: List assumptions and known results × Wrong proof method
Set up one fresh exam-style question in which the learner must practise list assumptions and known results while watching specifically for wrong proof method. Separate what is given from what must be proved. Require an independent response before any model is shown so the actual decision becomes visible.
The chosen method creates unnecessary complexity or fails to cover cases. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Given a domain split, list all cases before proving. Check none are omitted. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 3: Choose a proof method × Conclusion mismatch
Set up one fresh exam-style question in which the learner must practise choose a proof method while watching specifically for conclusion mismatch. Decide whether direct reasoning, contradiction, contrapositive, induction, cases, algebra or geometry fits. Require an independent response before any model is shown so the actual decision becomes visible.
The proof establishes a related fact but not the target. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Compare the proved statement with the original target. Repair scope mismatches. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 4: Start from accepted facts × Circular proof
Set up one fresh exam-style question in which the learner must practise start from accepted facts while watching specifically for circular proof. Use definitions, axioms, theorems or givens. Require an independent response before any model is shown so the actual decision becomes visible.
A later step depends on what the proof is trying to establish. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Classify arguments as examples, evidence or genuine proofs. Explain why. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 5: Justify each step × Case omission
Set up one fresh exam-style question in which the learner must practise justify each step while watching specifically for case omission. Every implication, equality or transformation should have a valid reason. Require an independent response before any model is shown so the actual decision becomes visible.
One branch of the domain is ignored. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 6: Cover all required cases × Example checking
Set up one fresh exam-style question in which the learner must practise cover all required cases while watching specifically for example checking. If the domain splits into cases, handle each or use a method that covers all. Require an independent response before any model is shown so the actual decision becomes visible.
Several cases are tested and called proof. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Given a domain split, list all cases before proving. Check none are omitted. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 7: Avoid circular reasoning × Unjustified leap
Set up one fresh exam-style question in which the learner must practise avoid circular reasoning while watching specifically for unjustified leap. Do not use the statement being proved as a reason for itself. Require an independent response before any model is shown so the actual decision becomes visible.
The proof skips a nontrivial implication. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Compare the proved statement with the original target. Repair scope mismatches. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 8: State the conclusion × Notation ambiguity
Set up one fresh exam-style question in which the learner must practise state the conclusion while watching specifically for notation ambiguity. End by explicitly connecting the chain to the required statement. Require an independent response before any model is shown so the actual decision becomes visible.
Variables or domains are not defined clearly. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Classify arguments as examples, evidence or genuine proofs. Explain why. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 9: Read the statement precisely × Assuming the conclusion
Set up one fresh exam-style question in which the learner must practise read the statement precisely while watching specifically for assuming the conclusion. Identify quantifiers, conditions, domain and conclusion. Require an independent response before any model is shown so the actual decision becomes visible.
The target statement appears as a premise. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 10: List assumptions and known results × Wrong proof method
Set up one fresh exam-style question in which the learner must practise list assumptions and known results while watching specifically for wrong proof method. Separate what is given from what must be proved. Require an independent response before any model is shown so the actual decision becomes visible.
The chosen method creates unnecessary complexity or fails to cover cases. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Given a domain split, list all cases before proving. Check none are omitted. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 11: Choose a proof method × Conclusion mismatch
Set up one fresh exam-style question in which the learner must practise choose a proof method while watching specifically for conclusion mismatch. Decide whether direct reasoning, contradiction, contrapositive, induction, cases, algebra or geometry fits. Require an independent response before any model is shown so the actual decision becomes visible.
The proof establishes a related fact but not the target. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Compare the proved statement with the original target. Repair scope mismatches. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 12: Start from accepted facts × Circular proof
Set up one fresh exam-style question in which the learner must practise start from accepted facts while watching specifically for circular proof. Use definitions, axioms, theorems or givens. Require an independent response before any model is shown so the actual decision becomes visible.
A later step depends on what the proof is trying to establish. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Classify arguments as examples, evidence or genuine proofs. Explain why. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 13: Justify each step × Case omission
Set up one fresh exam-style question in which the learner must practise justify each step while watching specifically for case omission. Every implication, equality or transformation should have a valid reason. Require an independent response before any model is shown so the actual decision becomes visible.
One branch of the domain is ignored. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 14: Cover all required cases × Example checking
Set up one fresh exam-style question in which the learner must practise cover all required cases while watching specifically for example checking. If the domain splits into cases, handle each or use a method that covers all. Require an independent response before any model is shown so the actual decision becomes visible.
Several cases are tested and called proof. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Given a domain split, list all cases before proving. Check none are omitted. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 15: Avoid circular reasoning × Unjustified leap
Set up one fresh exam-style question in which the learner must practise avoid circular reasoning while watching specifically for unjustified leap. Do not use the statement being proved as a reason for itself. Require an independent response before any model is shown so the actual decision becomes visible.
The proof skips a nontrivial implication. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Compare the proved statement with the original target. Repair scope mismatches. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 16: State the conclusion × Notation ambiguity
Set up one fresh exam-style question in which the learner must practise state the conclusion while watching specifically for notation ambiguity. End by explicitly connecting the chain to the required statement. Require an independent response before any model is shown so the actual decision becomes visible.
Variables or domains are not defined clearly. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Classify arguments as examples, evidence or genuine proofs. Explain why. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 17: Read the statement precisely × Assuming the conclusion
Set up one fresh exam-style question in which the learner must practise read the statement precisely while watching specifically for assuming the conclusion. Identify quantifiers, conditions, domain and conclusion. Require an independent response before any model is shown so the actual decision becomes visible.
The target statement appears as a premise. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 18: List assumptions and known results × Wrong proof method
Set up one fresh exam-style question in which the learner must practise list assumptions and known results while watching specifically for wrong proof method. Separate what is given from what must be proved. Require an independent response before any model is shown so the actual decision becomes visible.
The chosen method creates unnecessary complexity or fails to cover cases. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Given a domain split, list all cases before proving. Check none are omitted. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 19: Choose a proof method × Conclusion mismatch
Set up one fresh exam-style question in which the learner must practise choose a proof method while watching specifically for conclusion mismatch. Decide whether direct reasoning, contradiction, contrapositive, induction, cases, algebra or geometry fits. Require an independent response before any model is shown so the actual decision becomes visible.
The proof establishes a related fact but not the target. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Compare the proved statement with the original target. Repair scope mismatches. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 20: Start from accepted facts × Circular proof
Set up one fresh exam-style question in which the learner must practise start from accepted facts while watching specifically for circular proof. Use definitions, axioms, theorems or givens. Require an independent response before any model is shown so the actual decision becomes visible.
A later step depends on what the proof is trying to establish. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Classify arguments as examples, evidence or genuine proofs. Explain why. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 21: Justify each step × Case omission
Set up one fresh exam-style question in which the learner must practise justify each step while watching specifically for case omission. Every implication, equality or transformation should have a valid reason. Require an independent response before any model is shown so the actual decision becomes visible.
One branch of the domain is ignored. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 22: Cover all required cases × Example checking
Set up one fresh exam-style question in which the learner must practise cover all required cases while watching specifically for example checking. If the domain splits into cases, handle each or use a method that covers all. Require an independent response before any model is shown so the actual decision becomes visible.
Several cases are tested and called proof. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Given a domain split, list all cases before proving. Check none are omitted. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 23: Avoid circular reasoning × Unjustified leap
Set up one fresh exam-style question in which the learner must practise avoid circular reasoning while watching specifically for unjustified leap. Do not use the statement being proved as a reason for itself. Require an independent response before any model is shown so the actual decision becomes visible.
The proof skips a nontrivial implication. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Compare the proved statement with the original target. Repair scope mismatches. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 24: State the conclusion × Notation ambiguity
Set up one fresh exam-style question in which the learner must practise state the conclusion while watching specifically for notation ambiguity. End by explicitly connecting the chain to the required statement. Require an independent response before any model is shown so the actual decision becomes visible.
Variables or domains are not defined clearly. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Classify arguments as examples, evidence or genuine proofs. Explain why. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.
Workshop 25: Read the statement precisely × Assuming the conclusion
Set up one fresh exam-style question in which the learner must practise read the statement precisely while watching specifically for assuming the conclusion. Identify quantifiers, conditions, domain and conclusion. Require an independent response before any model is shown so the actual decision becomes visible.
The target statement appears as a premise. After correction, change one meaningful feature—topic, wording, evidence, mark allocation, numbers, source or context. Then use this related exercise: Find where a flawed proof assumes its conclusion. Repair the dependency. Finish with a delayed retest so success cannot be explained only by immediate memory of the correction.