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Proof step 32 from proof shiftright-rec-pos (previous step)

mklist(false, i→n(i0)) + false ' = false ' + bits, 0 ≤ i0 ⊦ bits2uint(firstn(1, (mklist(false, i→n(i0)) + false ' + false ' + true ').rest)) = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [mklist(false, i→n(i0)) + false ' + false ' + true ', boolvar, bits0] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ boolvar ' ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: mklist(false, i→n(i0)) + false ' + false ' + true ', boolvar, bits0