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Proof step 36 from proof int2bits-len-mon (previous step)

0 ≤ j, 0 < j, i + 1 < j, 1 < j, 0 ≤ j, # uint2bits(j) < # uint2bits(~(i + 1)), i < 0, 0 < j + i, i < j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: uint2bits-len-mon-02 rotate: F subst: [i, j] → [~(i + 1), j]

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;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i; Used terms: ~(i + 1), j