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Proof step 19 from proof int2bits-len-mon (previous step)

0 ≤ i, j < 0, j < i, i + j < 0, # int2bits(~(j + 1)) < # uint2bits(i) ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 21:
0 ≤ ~(j + 1), 0 ≤ i, j < 0, j < i, i + j < 0, # uint2bits(~(j + 1)) < # uint2bits(i) ⊦ j = 0

Rule argument

name: int2bits-pos rotate: F subst: [i] → [~(j + 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 → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: ~(j + 1)