Proof: Simplify If
Let's prove the following theorem:
if (3 ⋅ x) + 20 = 4 ⋅ x, then 20 = x
Proof:
Given
1 | (3 ⋅ x) + 20 = 4 ⋅ x |
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# | Claim | Reason |
---|---|---|
1 | (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) | if (3 ⋅ x) + 20 = 4 ⋅ x, then (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) |
2 | (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20 | (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20 |
3 | 20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) | if (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20 and (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x), then 20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) |
4 | (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x | (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x |
5 | 20 = x | if 20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) and (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x, then 20 = x |
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