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Proof step 11 from proof sgn-length-02 (previous step)

# sgn(bits0) < 2 + # bits0, 3 + # bits0 ≤ # sgn(boolvar ' + bits0) ⊦ bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
bits ≠ [], bits.first ↔ boolvar ⊦ sgn(boolvar ' + bits) = sgn(bits)
Proof step 13:
¬(bits0 ≠ [] ∧ (bits0.first ↔ boolvar)), # sgn(bits0) < 2 + # bits0, 3 + # bits0 ≤ # sgn(boolvar ' + bits0) ⊦ bits0 = []

Rule argument

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

Additional information

Used simplifier rules: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bits0, boolvar