Proof: Algebra 10

Let's prove the following theorem:

(s ⋅ s) - ((s ⋅ s) / 4) = (3 / 4) ⋅ (s ⋅ s)

Proof:

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Proof Table
# Claim Reason
1 s ⋅ s = (s ⋅ s) ⋅ 1 s ⋅ s = (s ⋅ s) ⋅ 1
2 4 / 4 = 1 4 / 4 = 1
3 (s ⋅ s) ⋅ (4 / 4) = (s ⋅ s) ⋅ 1 if 4 / 4 = 1, then (s ⋅ s) ⋅ (4 / 4) = (s ⋅ s) ⋅ 1
4 s ⋅ s = (s ⋅ s) ⋅ (4 / 4) if s ⋅ s = (s ⋅ s) ⋅ 1 and (s ⋅ s) ⋅ (4 / 4) = (s ⋅ s) ⋅ 1, then s ⋅ s = (s ⋅ s) ⋅ (4 / 4)
5 ((s ⋅ s) ⋅ (4 / 4)) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ ((4 / 4) + ((-1) / 4)) ((s ⋅ s) ⋅ (4 / 4)) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ ((4 / 4) + ((-1) / 4))
6 (4 / 4) + ((-1) / 4) = 3 / 4 (4 / 4) + ((-1) / 4) = 3 / 4
7 ((s ⋅ s) ⋅ (4 / 4)) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ (3 / 4) if ((s ⋅ s) ⋅ (4 / 4)) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ ((4 / 4) + ((-1) / 4)) and (4 / 4) + ((-1) / 4) = 3 / 4, then ((s ⋅ s) ⋅ (4 / 4)) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ (3 / 4)
8 (s ⋅ s) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ (3 / 4) if ((s ⋅ s) ⋅ (4 / 4)) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ (3 / 4) and s ⋅ s = (s ⋅ s) ⋅ (4 / 4), then (s ⋅ s) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ (3 / 4)
9 (s ⋅ s) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) - ((s ⋅ s) / 4) (s ⋅ s) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) - ((s ⋅ s) / 4)
10 (s ⋅ s) - ((s ⋅ s) / 4) = (s ⋅ s) ⋅ (3 / 4) if (s ⋅ s) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) - ((s ⋅ s) / 4) and (s ⋅ s) + ((s ⋅ s) ⋅ ((-1) / 4)) = (s ⋅ s) ⋅ (3 / 4), then (s ⋅ s) - ((s ⋅ s) / 4) = (s ⋅ s) ⋅ (3 / 4)
11 (s ⋅ s) ⋅ (3 / 4) = (3 / 4) ⋅ (s ⋅ s) (s ⋅ s) ⋅ (3 / 4) = (3 / 4) ⋅ (s ⋅ s)
12 (s ⋅ s) - ((s ⋅ s) / 4) = (3 / 4) ⋅ (s ⋅ s) if (s ⋅ s) - ((s ⋅ s) / 4) = (s ⋅ s) ⋅ (3 / 4) and (s ⋅ s) ⋅ (3 / 4) = (3 / 4) ⋅ (s ⋅ s), then (s ⋅ s) - ((s ⋅ s) / 4) = (3 / 4) ⋅ (s ⋅ s)

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