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Proof step 15 from proof cast-mod-neg-low (previous step)

j % 2 < 0, j < ~1, j % 2 < ~1, j < 0, 1 ≤ # int2bits(j) ⊦ bits2int(int2bits(j).last ') = 2 + j % 2, j = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ j % 2 ≠ 0 ∧ j < ~1 → int2bits(j) = int2bits(j / 2 - 1) + true '
Proof step 17:
j % 2 ≠ 0 ∧ j < ~1, j % 2 < 0, j < ~1, j % 2 < ~1, j < 0, 1 ≤ #(int2bits(j / 2 - 1) + true ') ⊦ bits2int((int2bits(j / 2 - 1) + true ').last ') = 2 + j % 2, j = ~1

Rule argument

seq: ⊦ j % 2 ≠ 0 ∧ j < ~1 → int2bits(j) = int2bits(j / 2 - 1) + true ' subst: [j] → [j] rotate: F spec: int2bits inst: name: int2bits-rec-neg-03

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) Used terms: j