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Proof step 2 from proof succ-falsein-02 (previous step)

bits.last ∨ false ∈ bits.butlast ⊦ bits = [], false ∈ bits +1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≠ # bits ∧ bits.last → bits +1 = bits.butlast +1 + false '

Rule argument

name: succ-rec-02 rotate: F subst: [bits] → [bits]

Additional information

Used simplifier rules: succ-zero-03: ⊦ bits ≠ [] ∧ ¬ bits.last → bits +1 = bits.butlast + true;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # bits = 0 ↔ bits = []; Used terms: bits