Proof: Greater Than Substitution
Let's prove the following theorem:
if the following are true:
- x is greater than y
- minimum value of stack z = y
then x is greater than (minimum value of stack z)
Proof:
Given
1 | x is greater than y |
---|---|
2 | minimum value of stack z = y |
# | Claim | Reason |
---|---|---|
1 | y = minimum value of stack z | if minimum value of stack z = y, then y = minimum value of stack z |
2 | x is greater than y = x is greater than (minimum value of stack z) | if y = minimum value of stack z, then x is greater than y = x is greater than (minimum value of stack z) |
3 | x is greater than (minimum value of stack z) | if x is greater than y and x is greater than y = x is greater than (minimum value of stack z), then x is greater than (minimum value of stack z) |
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