Proof: Multiply by 1 Less

Let's prove the following theorem:

if a ⋅ 1 < b, then a < b

Proof:

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Given
1 a ⋅ 1 < b
Proof Table
# Claim Reason
1 a ⋅ 1 = a a ⋅ 1 = a
2 a < b if a ⋅ 1 = a and a ⋅ 1 < b, then a < b

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