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Proof step 5 from proof band-31-pos (previous step)

i < 32, 0 ≤ i, false ∈ int2bits(31).rest ⊦ band(i, 31) = i

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
int2bits(31) = boolvar + bits ∧ int2bits(31) ≠ [], i < 32, 0 ≤ i, false ∈ bits ⊦ band(i, 31) = i

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [int2bits(31), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ int2bits(j) ≠ [];%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: int2bits(31), boolvar, bits