Double Transitive Property Less

Proof: Double Transitive Property Less

Let's prove the following theorem:

if the following are true:
  • a < b
  • a = x
  • b = y

then x < y

Proof:

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Given
1 a < b
2 a = x
3 b = y
Proof Table
# Claim Reason
1 a < b = x < b if a = x, then a < b = x < b
2 x < b = x < y if b = y, then x < b = x < y
3 a < b = x < y if a < b = x < b and x < b = x < y, then a < b = x < y
4 x < y if a < b and a < b = x < y, then x < y

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