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Proof step 16 from proof ubits2ubits-def (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ¬ true ∈ bits ∧ bits ≠ [] → sgn(bits) = false '

Rule argument

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

Additional information

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