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Proof step 3 from proof bits2int-neg-1bit-01 (previous step)

⊦ bits.first ∧ bits ≠ [] → bits2int(sgn(true ' + bits)) = bits2int(bits)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)

Rule argument

seq: bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits) subst: [bits, boolvar] → [bits, true] rotate: F spec: bitopsaux inst: name: sgn-rec-01

Additional information

Used simplifier rules: bits2int-sgn: ⊦ bits2int(sgn(bits)) = bits2int(bits);%bits2int-neg: ⊦ bits2int(true ' + bits) = ~ bits2uint(bitsinvert(true + bits) +1);%bits2int-sgn: ⊦ bits2int(sgn(bits)) = bits2int(bits);%bits2int-inj: ⊦ bits ≠ [] ∧ bits0 ≠ [] → (bits2int(bits) = bits2int(bits0) ↔ sgn(bits) = sgn(bits0));% ⊦ boolvar + bits = boolvar ' + bits;% ⊦ bitsinvert(true ' + bits) = false + bitsinvert(bits);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ~ i = j ↔ i + j = 0; Used terms: bits, true