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Proof step 21 from proof intshiftleft-is-mult (previous step)

j < 32, 0 < j, 0 ≤ i ⊦ 2 ^ j * bits2uint(int2bits(i)) = i * 2 ^ j, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 0 ≤ i → int2bits(i) = uint2bits(i)

Rule argument

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

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ 0 ≤ i → bits2uint(uint2bits(i)) = i; Used terms: i