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Proof step 7 from proof sgn-mklist-03 (previous step)

∀ boolvar. sgn(mklist(boolvar, m)) = boolvar ' ⊦ sgn(boolvar ' + mklist(boolvar, m)) = boolvar ', m = 0, mklist(boolvar, m).first ↔ boolvar

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [mklist(boolvar, m), boolvar0, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ boolvar + bits = boolvar ' + bits;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ mklist(boolvar0, n) → (boolvar ↔ boolvar0); (forward)%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: mklist(boolvar, m), boolvar0, bits