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Proof step 5 from proof int2bits-lslen-03 (previous step)

i < ~1, i < 0 ⊦ # int2bits(~(i + 1)) < m ↔ ¬ i + 2 ^ (n→i(m) - 2) < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < i → (# int2bits(i) < m ↔ i < 2 ^ (n→i(m) - 2))

Rule argument

name: int2bits-lslen rotate: F subst: [m, i] → [m, ~(i + 1)]

Additional information

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