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Proof step 9 from proof int2bits-rest (previous step)

sgn(bitsinvert(uint2bits(~ j)) +1).rest = [], j < 0 ⊦ j = ~1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 1 < i → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 11:
1 < ~ j, sgn(bitsinvert(uint2bits(~ j / 2) + (~ j % 2 = 1)) +1).rest = [], j < 0 ⊦ j = ~1, j = 0

Rule argument

name: uint2bits-rec rotate: F subst: [i] → [~ j]

Additional information

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