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Proof step 12 from proof uint2bits-add-high-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
int2bits(j0) = boolvar ' + bits, 0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0, boolvar ∈ int2bits(j0) ⊦ sgn(bits) = sgn(false ' + fillsgn(i→n(i), bits)), ¬ fillsgn(i→n(i), bits).first ∧ (i ≠ 0 ∨ bits ≠ [])

Rule argument

Additional information

Used simplifier rules: int2bits-not-empty: ⊦ int2bits(j) ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ boolvar + bits = boolvar ' + bits;