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Proof step 12 from proof intshiftleft-is-mult (previous step)

j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(j))) = i * 2 ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ # bits0 ≠ 0 ∧ # bits ≠ 0 ∧ ¬ bits.first → bits2int(bits + bits0) = bits2uint(bits) * 2 ^ n→i(# bits0) + bits2uint(bits0)
Proof step 14:
¬(# mklist(false, i→n(j)) ≠ 0 ∧ # int2bits(i) ≠ 0 ∧ ¬ int2bits(i).first), j < 32, 0 ≤ j ⊦ bits2int(int2bits(i) + mklist(false, i→n(j))) = i * 2 ^ j
Proof step 20:
# mklist(false, i→n(j)) ≠ 0 ∧ # int2bits(i) ≠ 0 ∧ ¬ int2bits(i).first, j < 32, 0 ≤ j ⊦ bits2uint(int2bits(i)) * 2 ^ n→i(# mklist(false, i→n(j))) + bits2uint(mklist(false, i→n(j))) = i * 2 ^ j

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(j)), int2bits(i)] rotate: F spec: int2bits inst: name: bits2int-split

Additional information

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