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Proof step 7 from proof bint-and-011x-bits2unit (previous step)

~2147483648 ≤ i, i < 0 ⊦ bits2uint(fillsgn(32, int2bits(i))) = band(i, 4294967295)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % (i + 1) + i
Proof step 9:
i < 0 ∧ ¬ false ∈ int2bits(4294967295).rest ∧ 0 ≤ 4294967295, ~2147483648 ≤ i, i < 0 ⊦ bits2uint(fillsgn(32, int2bits(i))) = (i + 1) % (4294967295 + 1) + 4294967295

Rule argument

seq: ⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % (i + 1) + i subst: [i, j] → [4294967295, i] rotate: F spec: intops inst: name: band-011x-neg-02

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ false ∈ int2bits(4294967295).rest; Used terms: 4294967295, i