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Proof step 7 from proof int2bits-len-add (previous step)

0 ≤ i, j < 0, j0 < 0, 0 < 2 ^ i + j0, 0 < 2 ^ i * j + j0 ⊦ # int2bits(~(2 ^ i * j + j0)) = # int2bits(~ j) + i→n(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ j < 0 ∧ j0 ≤ 0 → ¬ 0 < i * j + j0 subst: [j0, j, i] → [j0, j, 2 ^ i] rotate: F spec: int-mult inst: name: zero-gr-add-01

Additional information

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