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Proof step 3 from proof intshiftleft-is-mult-01 (previous step)

⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 31)))) = i * 2 ^ band(j, 31)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 5:
¬(# mklist(false, i→n(band(j, 31))) ≠ 0 ∧ # int2bits(i) ≠ 0 ∧ ¬ int2bits(i).first) ⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 31)))) = i * 2 ^ band(j, 31)
Proof step 34:
# mklist(false, i→n(band(j, 31))) ≠ 0 ∧ # int2bits(i) ≠ 0 ∧ ¬ int2bits(i).first ⊦ bits2uint(int2bits(i)) * 2 ^ n→i(# mklist(false, i→n(band(j, 31)))) + bits2uint(mklist(false, i→n(band(j, 31)))) = i * 2 ^ band(j, 31)

Rule argument

seq: ⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0) subst: [bits0, bits] → [mklist(false, i→n(band(j, 31))), int2bits(i)] rotate: F spec: int2bits inst: name: bits2int-split

Additional information

Used terms: mklist(false, i→n(band(j, 31))), int2bits(i)