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Proof step 26 from proof band-011x-neg-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
0 ≤ i, 0 < j, i + 1 < j, abs(1 - j) ≤ i ⊦ (1 - j) % (i + 1) = (i + 2 - j) % (i + 1), j = 1, false ∈ int2bits(i).rest

Rule argument

Additional information

Used simplifier rules: ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ 0 < i → (i ≤ 1 ↔ i = 1);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + 0 = i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + (j - i0) = i + j - i0;