Proof: Simplify4

Let's prove the following theorem:

((x ⋅ 4) ⋅ 2) - 4 = (x ⋅ 8) - 4

Proof:

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Proof Table
# Claim Reason
1 4 ⋅ 2 = 8 4 ⋅ 2 = 8
2 (x ⋅ 4) ⋅ 2 = x ⋅ (4 ⋅ 2) (x ⋅ 4) ⋅ 2 = x ⋅ (4 ⋅ 2)
3 x ⋅ (4 ⋅ 2) = x ⋅ 8 if 4 ⋅ 2 = 8, then x ⋅ (4 ⋅ 2) = x ⋅ 8
4 (x ⋅ 4) ⋅ 2 = x ⋅ 8 if (x ⋅ 4) ⋅ 2 = x ⋅ (4 ⋅ 2) and x ⋅ (4 ⋅ 2) = x ⋅ 8, then (x ⋅ 4) ⋅ 2 = x ⋅ 8
5 ((x ⋅ 4) ⋅ 2) - 4 = (x ⋅ 8) - 4 if (x ⋅ 4) ⋅ 2 = x ⋅ 8, then ((x ⋅ 4) ⋅ 2) - 4 = (x ⋅ 8) - 4

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