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Proof step 30 from proof band-011x-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
0 < j, 0 ≤ i, i < j ⊦ i % j = i
Proof step 32:
0 < i + 1 ∧ 0 ≤ i + 1 - j ∧ i + 1 - j < i + 1, j ≤ i + 1, 0 < j, 0 ≤ i ⊦ (1 - j) % (i + 1) + i = i + 1 - j, false ∈ int2bits(i).rest

Rule argument

seq: 0 < j, 0 ≤ i, i < j ⊦ i % j = i subst: [j, i] → [i + 1, i + 1 - j] rotate: F spec: int-div inst: name: mod-zero-03

Additional information

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