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Proof step 2 from proof bits2int-rec-03 (previous step)

bits.first, false ∈ bits ⊦ bits2int(bits + true ') = bits2int(bits) * 2 + 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
bits = boolvar + bits0 ∧ bits ≠ [], boolvar, false ∈ bits ⊦ bits2int(bits + true ') = bits2int(bits) * 2 + 1

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits, boolvar, bits0] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

Used simplifier rules: bits2int-one: ⊦ bits2int(true ') = ~1;% ⊦ [] + bits = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ i + 1 = ~1 ↔ i + 1 + 1 = 0;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 2 * i = 0 ↔ i = 0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ ¬ boolvar ∈ [];%⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: bits, boolvar, bits0