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Proof step 8 from proof fill-sgn (previous step)

# sgn(boolvar ' + bits0) ≤ 1 + # bits0 ⊦ mklist(boolvar, 1 + # bits0 - # sgn(boolvar ' + bits0)) + sgn(boolvar ' + bits0) = boolvar ' + bits0

User applied rule insert lemma

And obtained the following new goals

Proof step 9:
⊦ bits ≠ [] ↔ (∃ n. bits = mklist(bits.first, n) + sgn(bits) ∧ bits ≠ [])
Proof step 10:
boolvar ' + bits0 ≠ [] ↔ (∃ n. boolvar ' + bits0 = mklist((boolvar ' + bits0).first, n) + sgn(boolvar ' + bits0) ∧ boolvar ' + bits0 ≠ []), # sgn(boolvar ' + bits0) ≤ 1 + # bits0 ⊦ mklist(boolvar, 1 + # bits0 - # sgn(boolvar ' + bits0)) + sgn(boolvar ' + bits0) = boolvar ' + bits0

Rule argument

name: sgn-ex subst: [bits] → [boolvar ' + bits0]

Additional information

Used terms: boolvar ' + bits0