Proof: Inverse Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	s ⋅ (1 / 2) = s / 2	s ⋅ (1 / 2) = s / 2 (division_theorem)
2	(s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = (s / 2) ⋅ (s / 2)	if s ⋅ (1 / 2) = s / 2 and s ⋅ (1 / 2) = s / 2, then (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = (s / 2) ⋅ (s / 2) (Substitute Two Variables Theorem)
3	(s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2)	(s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) (reorder_terms_8)
4	((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) = (s / 2) ⋅ (s / 2)	if (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) and (s ⋅ (1 / 2)) ⋅ (s ⋅ (1 / 2)) = (s / 2) ⋅ (s / 2), then ((s ⋅ s) ⋅ (1 / 2)) ⋅ (1 / 2) = (s / 2) ⋅ (s / 2) (Transitive Property of Equality Variation 2)

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