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Proof step 12 from proof intshiftrzero-prop-01 (previous step)

~2147483648 ≤ i, i < 0, false ∈ int2bits(31).rest ⊦ band(j, 31) = 0, bits2int(sublist(0, # fillsgn(32, int2bits(i)), mklist(false, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) = bits2int(int2bits(2) + mklist(false, i→n(band(~(j + 1), 31)))) + (i i>> j)

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] → [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