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Proof step 6 from proof succ-first-01 (previous step)

true ∈ (boolvar ' +1 + bitsinvert(bits0)).rest ⊦ (boolvar ' +1 + bitsinvert(bits0)).first ↔ boolvar, false ∈ bits0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
boolvar ' +1 + bitsinvert(bits0) = boolvar0 + bits ∧ boolvar ' +1 + bitsinvert(bits0) ≠ [], true ∈ bits ⊦ boolvar0 ↔ boolvar, false ∈ bits0

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [boolvar ' +1 + bitsinvert(bits0), boolvar0, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: succ-empty-01: ⊦ ¬ bits +1 ≠ [] ↔ false;%inv-empty: ⊦ bitsinvert(bits) = [] ↔ bits = [];% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: boolvar ' +1 + bitsinvert(bits0), boolvar0, bits