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Proof step 24 from proof uint2bits-add-high-02 (previous step)

int2bits(j0).rest = [], j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i ⊦ i = 0, mklist(false, i→n(i)).first

User applied rule insert elim lemma

And obtained the following new goals

Proof step 25:
int2bits(j0) = boolvar + bits ∧ int2bits(j0) ≠ [], bits = [], j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i ⊦ i = 0, mklist(false, i→n(i)).first

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [int2bits(j0), boolvar, bits] rotate: T spec: list-data inst: bitlista name: elim-list

Additional information

Used simplifier rules: int2bits-not-empty: ⊦ int2bits(j) ≠ [];%⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: int2bits(j0), boolvar, bits