Proof: Divide Each Side

Let's prove the following theorem:

if the following are true:
  • a ⋅ b = c
  • not (b = 0)

then a = c / b

Proof:

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Given
1 a ⋅ b = c
2 not (b = 0)
Proof Table
# Claim Reason
1 (a ⋅ b) / b = c / b if a ⋅ b = c, then (a ⋅ b) / b = c / b
2 (a ⋅ b) / b = a if not (b = 0), then (a ⋅ b) / b = a
3 a = c / b if (a ⋅ b) / b = a and (a ⋅ b) / b = c / b, then a = c / b

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