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Proof step 47 from proof intshiftleft-is-mult-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ ¬ j < 0 → abs(j) = j
Proof step 49:
¬ ¬ 31 + (j + 1) % 32 < 0, 0 < i, j < 0 ⊦ ~31 = (j + 1) % 32, i = 0, 2 ^ abs(31 + (j + 1) % 32) = 2 ^ (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; Used terms: 31 + (j + 1) % 32