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Proof step 22 from proof intshiftrsign-if (previous step)

# int2bits(i) = n + i→n(band(j, 31)), i→n(band(j, 31)) < # int2bits(i) ⊦ bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, n, int2bits(i))) = bits2int(sublist(0, n, int2bits(i))), n = 0, sublist(0, n, int2bits(i)).first ↔ ¬ 0 ≤ i

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] → [sublist(0, n, int2bits(i)), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: ⊦ sublist(0, n, bits) = [] ↔ n = 0;%bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: sublist(0, n, int2bits(i)), boolvar, bits