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Proof step 41 from proof cast-mod-neg-high (previous step)

# int2bits(j) = i→n(i) + 1, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, 0 < j + 2 ^ i, j < ~1 ⊦ i = 1, j = ~1, 2 ^ i + j = j % 2 ^ i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ abs(i) < j → i % j = i

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [2 ^ i, j] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i = i + j ↔ j = 0;% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < j + i0 ∧ j < j0 → i < j0 + i0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 2 ^ i, j