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Proof step 39 from proof ubits2ubits-def (previous step)

uint2bits(bits2uint(bits0)) = sgn(false ' + bits0), 0 ≤ bits2uint(bits0), 0 < bits2uint(bits0), ∀ bits1. # bits1 < #(bits0 + true ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ uint2bits(bits2uint(bits0)) + true ' = sgn(false ' + bits0 + true ')

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: boolvar ↔ ¬ boolvar0 ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 ' subst: [boolvar0, bits, boolvar] → [true, bits0, false] rotate: F spec: bitopsaux inst: name: sgn-last-01

Additional information

Used simplifier rules: ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: true, bits0, false