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Proof step 31 from proof int2bits-len-mon (previous step)

i < j, 0 < j + i, i < 0, # int2bits(j) < # int2bits(~(i + 1)), 0 ≤ j, 1 < j, i + 1 < j, 0 < j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

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