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Proof step 15 from proof int2bits-len-add (previous step)

0 ≤ i, j < 0, j0 < 0, j * 2 ^ i + j0 ≤ 0, 0 < 2 ^ i + j0 ⊦ # uint2bits(~ j) = # int2bits(~ j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)

Rule argument

name: int2bits-pos rotate: F subst: [i] → [~ j]

Additional information

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