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Proof step 29 from proof intshiftleft-is-mult-01 (previous step)

i < 0, j < 0 ⊦ ~31 = (j + 1) % 32, 2 ^ abs(31 + (j + 1) % 32) * (i + 1) = 2 ^ (31 + (j + 1) % 32) * i + 2 ^ abs(31 + (j + 1) % 32), false ∈ int2bits(31).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ ¬ j < 0 → abs(j) = j
Proof step 31:
¬ ¬ 31 + (j + 1) % 32 < 0, i < 0, j < 0 ⊦ ~31 = (j + 1) % 32, 2 ^ abs(31 + (j + 1) % 32) * (i + 1) = 2 ^ (31 + (j + 1) % 32) * i + 2 ^ abs(31 + (j + 1) % 32), false ∈ int2bits(31).rest

Rule argument

seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [31 + (j + 1) % 32] rotate: F spec: int-abs inst: name: Abs-pos

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0; Used terms: 31 + (j + 1) % 32