Proof: Shuffle Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	3 / 4 = 3 ⋅ (1 / 4)	3 / 4 = 3 ⋅ (1 / 4) (Division is Multiplication by Inverse)
2	(3 / 4) ⋅ (s ⋅ s) = (3 ⋅ (1 / 4)) ⋅ (s ⋅ s)	if 3 / 4 = 3 ⋅ (1 / 4), then (3 / 4) ⋅ (s ⋅ s) = (3 ⋅ (1 / 4)) ⋅ (s ⋅ s) (Multiplicative Property of Equality)
3	(3 ⋅ (1 / 4)) ⋅ (s ⋅ s) = (3 ⋅ (s ⋅ s)) ⋅ (1 / 4)	(3 ⋅ (1 / 4)) ⋅ (s ⋅ s) = (3 ⋅ (s ⋅ s)) ⋅ (1 / 4) (Swap 2 and 3 Theorem)
4	(3 / 4) ⋅ (s ⋅ s) = (3 ⋅ (s ⋅ s)) ⋅ (1 / 4)	if (3 / 4) ⋅ (s ⋅ s) = (3 ⋅ (1 / 4)) ⋅ (s ⋅ s) and (3 ⋅ (1 / 4)) ⋅ (s ⋅ s) = (3 ⋅ (s ⋅ s)) ⋅ (1 / 4), then (3 / 4) ⋅ (s ⋅ s) = (3 ⋅ (s ⋅ s)) ⋅ (1 / 4) (Transitive Property of Equality)
5	(3 ⋅ (s ⋅ s)) ⋅ (1 / 4) = 3 ⋅ ((s ⋅ s) ⋅ (1 / 4))	(3 ⋅ (s ⋅ s)) ⋅ (1 / 4) = 3 ⋅ ((s ⋅ s) ⋅ (1 / 4)) (Associative Property of Multiplication)
6	(3 / 4) ⋅ (s ⋅ s) = 3 ⋅ ((s ⋅ s) ⋅ (1 / 4))	if (3 / 4) ⋅ (s ⋅ s) = (3 ⋅ (s ⋅ s)) ⋅ (1 / 4) and (3 ⋅ (s ⋅ s)) ⋅ (1 / 4) = 3 ⋅ ((s ⋅ s) ⋅ (1 / 4)), then (3 / 4) ⋅ (s ⋅ s) = 3 ⋅ ((s ⋅ s) ⋅ (1 / 4)) (Transitive Property of Equality)

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