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Proof step 2 from proof succ-len (previous step)

false ∈ bits ⊦ # bits +1 = # bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ boolvar ∈ bits ↔ (∃ bits0, bits1. bits = bits0 + boolvar ' + bits1 ∧ ¬ boolvar ∈ bits1)

Rule argument

seq: ⊦ boolvar ∈ bits ↔ (∃ bits0, bits1. bits = bits0 + boolvar ' + bits1 ∧ ¬ boolvar ∈ bits1) subst: [bits, boolvar] → [bits, false] rotate: F spec: list inst: bitlista name: lastoc-rew

Additional information

Used simplifier rules: succ-prefix: ⊦ (bits + false ' + bits0)+1 = bits + (false ' + bits0)+1;%succ-zeros-01: ⊦ ¬ false ∈ bits0 → (bits + bits0)+1 = bits +1 + bitsinvert(bits0);%succ-one: ⊦ false ' +1 = true ';%inv-len: ⊦ # bitsinvert(bits) = # bits;% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (m + n0) + n1 = m + n0 + n1; Used terms: bits, false