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Proof step 29 from proof ubits2ubits-def (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
boolvar ↔ ¬ boolvar0 ⊦ sgn(boolvar ' + bits + boolvar0 ') = sgn(boolvar ' + bits) + boolvar0 '
Proof step 31:
false ↔ ¬ true, ∀ bits1. # bits1 < #(bits0 + true ') → true → uint2bits(bits2uint(bits1)) = sgn(false ' + bits1) ⊦ false ' + true ' = sgn(false ' + bits0) + true ', true ∈ bits0

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 terms: true, bits0, false