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Proof step 5 from proof bint-band-zero (previous step)

band(4294967295, i) = 0, ~2147483648 ≤ i, i < 0 ⊦ i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i ∈bint ∧ i < 0 → band(4294967295, i) = i + 4294967296

Rule argument

name: bint-band-011x-neg rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: inbint: ⊦ i ∈bint ↔ ~2147483648 ≤ i ∧ i ≤ 2147483647;%inbint: ⊦ i ∈bint ↔ ~2147483648 ≤ i ∧ i ≤ 2147483647;% ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j ∧ ¬ i0 < j → ¬ i0 < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; Used terms: i