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Proof step 20 from proof band-011x-neg-03 (previous step)

0 ≤ i, 0 < j, i + 1 < j ⊦ (1 - j) % (i + 1) = (2 + i - j) % (i + 1), false ∈ int2bits(i).rest

User applied rule cut formula

And obtained the following new goals

Proof step 21:
2 + i - j = (1 - j) + i + 1, 0 ≤ i, 0 < j, i + 1 < j ⊦ (1 - j) % (i + 1) = (2 + i - j) % (i + 1), false ∈ int2bits(i).rest

Rule argument

fma: 2 + i - j = (1 - j) + i + 1

Additional information

Used simplifier rules: ⊦ i + (j - i0) = i + j - i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: 2 + i - j = (1 - j) + i + 1