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Proof step 18 from proof uint2bits-add-high-02 (previous step)

int2bits(j0) = true ' + bits, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i, bits.first ⊦ bits = [], j0 = 0, sgn(bits) = sgn(false ' + fillsgn(i→n(i), bits))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
bits = boolvar + bits0, int2bits(j0) = true ' + bits, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 ≤ j0 + 2 ^ i, boolvar ⊦ bits = [], j0 = 0, sgn(bits) = sgn(false ' + fillsgn(i→n(i), bits))

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits, boolvar, bits0] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

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