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Proof step 13 from proof bint-and-011x-bits2unit (previous step)

~2147483648 ≤ i, i < 0 ⊦ bits2uint(fillsgn(32, int2bits(i))) = 4294967296 + i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ bits ≠ [] ∧ bits.first → bits2uint(bits) = bits2int(bits) + 2 ^ n→i(# bits)
Proof step 15:
fillsgn(32, int2bits(i)) ≠ [] ∧ fillsgn(32, int2bits(i)).first, ~2147483648 ≤ i, i < 0 ⊦ bits2int(fillsgn(32, int2bits(i))) + 2 ^ n→i(# fillsgn(32, int2bits(i))) = 4294967296 + i

Rule argument

seq: ⊦ bits ≠ [] ∧ bits.first → bits2uint(bits) = bits2int(bits) + 2 ^ n→i(# bits) subst: [bits] → [fillsgn(32, int2bits(i))] rotate: F spec: int2bits inst: name: ubits2bits

Additional information

Used simplifier rules: ⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0;% ⊦ int2bits(j) ≠ [];% ⊦ fillsgn(n, int2bits(j)).first ↔ int2bits(j).first;% ⊦ j < 0 → int2bits(j).first; Used terms: fillsgn(32, int2bits(i))