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Proof step 24 from proof int2bits-2pot-04 (previous step)

0 < i, 0 < 2 ^ i, j < 2 ^ i, j < 0, j + 1 < 2 ^ i, j < i, j * 2 ^ i < i, j + 1 < i ⊦ sgn(bitsinvert(uint2bits(~ j)) +1 + mklist(false, i→n(i))) = int2bits(j) + mklist(false, i→n(i)), j = 0, i = 0, (¬ mklist(false, i→n(i)).first) ∈ bitsinvert(uint2bits(~ j)) +1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
mklist(false, i→n(i)) = boolvar + bits ∧ mklist(false, i→n(i)) ≠ [], 0 < i, 0 < 2 ^ i, j < 2 ^ i, j < 0, j + 1 < 2 ^ i, j < i, j * 2 ^ i < i, j + 1 < i ⊦ sgn(bitsinvert(uint2bits(~ j)) +1 + mklist(false, i→n(i))) = int2bits(j) + mklist(false, i→n(i)), j = 0, i = 0, (¬ boolvar) ∈ bitsinvert(uint2bits(~ j)) +1

Rule argument

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

Additional information

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