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Proof step 38 from proof intshiftleft-is-mult-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)
Proof step 40:
0 ≤ 31, 0 < i ⊦ band(j, 31) = 0, i = 0, 2 ^ abs(band(j, 31)) = 2 ^ band(j, 31), ¬ j < 0 ∧ ¬ 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