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

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

seq: ⊦ j < ~1 → int2bits(j) = int2bits((j - 1) / 2) + int2bits(j % 2) subst: [j] → [j] rotate: F spec: int2bits inst: name: int2bits-rec-neg-01

Additional information

Used terms: j