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Proof step 17 from proof intshiftleft-is-mult-01 (previous step)

i < 0 ⊦ band(j, 31) = 0, (i + 1) * 2 ^ abs(band(j, 31)) = 2 ^ abs(band(j, 31)) + i * 2 ^ band(j, 31), ¬ 0 ≤ j ∧ ¬ false ∈ int2bits(31).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 19:
0 ≤ 31, i < 0 ⊦ band(j, 31) = 0, (i + 1) * 2 ^ abs(band(j, 31)) = 2 ^ abs(band(j, 31)) + i * 2 ^ band(j, 31), ¬ 0 ≤ j ∧ ¬ false ∈ uint2bits(31).rest

Rule argument

seq: ⊦ 0 ≤ i → int2bits(i) = uint2bits(i) subst: [i] → [31] rotate: F spec: int2bits inst: name: int2bits-pos

Additional information

Used terms: 31