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Proof step 4 from proof sgn-length (previous step)

1 + # bits0 < # sgn(boolvar ' + bits0), ¬ # sgn(bits0) ≤ # bits0 → sgn(bits0) = [] ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 6:
¬(bits0 ≠ [] ∧ (bits0.first ↔ boolvar)), 1 + # bits0 < # sgn(boolvar ' + bits0), ¬ # sgn(bits0) ≤ # bits0 → sgn(bits0) = [] ⊦

Rule argument

name: sgn-rec-01 rotate: F subst: [bits, boolvar] → [bits0, boolvar]

Additional information

Used simplifier rules: sgn-not-empty: ⊦ bits ≠ [] → sgn(bits) ≠ [];% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bits0, boolvar