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Proof step 2 from proof intshiftleft-is-mult (previous step)

j < 32, 0 ≤ j ⊦ i i<< j = i * 2 ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i i<< j = bits2int(int2bits(i) + mklist(false, i→n(band(j, 31))))
Proof step 4:
j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 31)))) = i * 2 ^ j

Rule argument

name: intshiftleft rotate: F subst: [j, i] → [j, i]

Additional information

Used terms: j, i