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Proof step 32 from proof ubits2ubits-def (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits) = false '

Rule argument

seq: ⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits) = false ' subst: [bits] → [false ' + bits0] rotate: F spec: bitopsaux inst: name: sgn-zero

Additional information

Used simplifier rules: ⊦ ¬ boolvar ∈ bits → (boolvar ∈ boolvar0 ' + bits ↔ boolvar ↔ boolvar0);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ []; Used terms: false ' + bits0