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Proof step 5 from proof int2bits-len-mod2pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i ∧ 0 < j → (i % j ≤ 0 ↔ i % j = 0)

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 < j → (i % j ≤ 0 ↔ i % j = 0) subst: [j, i] → [2 ^ i, j] rotate: F spec: int-div inst: name: mod-zero-02

Additional information

Used simplifier rules: int2bits-zero: ⊦ int2bits(0) = false ';% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ # boolvar ' = 0 +1;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: 2 ^ i, j