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Proof step 72 from proof int2bits-add-high (previous step)

2 ^ n→i(# int2bits(1 - j)) + j = 2 ^ i0, 0 ≤ 2 ^ i * 2 ^ i0 + j0, 0 ≤ j0 + 2 ^ i, j < 0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, j * 2 ^ i + j0 < 0, 0 < i0 ⊦ sgn(true ' + fillsgn(i→n(i), int2bits(j0).rest)) = true ' + fillsgn(i→n(i), int2bits(j0).rest), i0 = 0, ∃ i0. 1 = 2 ^ i0 + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 73:
⊦ bits ≠ [] ∧ (bits.first ↔ ¬ boolvar) → sgn(boolvar ' + bits) = boolvar ' + bits
Proof step 74:
¬(fillsgn(i→n(i), int2bits(j0).rest) ≠ [] ∧ (fillsgn(i→n(i), int2bits(j0).rest).first ↔ ¬ true)), 2 ^ n→i(# int2bits(1 - j)) + j = 2 ^ i0, 0 ≤ 2 ^ i * 2 ^ i0 + j0, 0 ≤ j0 + 2 ^ i, j < 0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 < 0, 0 < 2 ^ i + j0, 0 ≤ i, j * 2 ^ i + j0 < 0, 0 < i0 ⊦ sgn(true ' + fillsgn(i→n(i), int2bits(j0).rest)) = true ' + fillsgn(i→n(i), int2bits(j0).rest), i0 = 0, ∃ i0. 1 = 2 ^ i0 + j

Rule argument

seq: ⊦ bits ≠ [] ∧ (bits.first ↔ ¬ boolvar) → sgn(boolvar ' + bits) = boolvar ' + bits subst: [bits, boolvar] → [fillsgn(i→n(i), int2bits(j0).rest), true] rotate: F spec: bitopsaux inst: name: sgn-base-03

Additional information

Used terms: fillsgn(i→n(i), int2bits(j0).rest), true