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Proof step 12 from proof fill-sgn (previous step)

#(boolvar ' + bits0) = #(mklist(boolvar, n) + sgn(boolvar ' + bits0)), boolvar ' + bits0 = mklist(boolvar, n) + sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ 1 + # bits0 ⊦ mklist(boolvar, 1 + # bits0 - # sgn(boolvar ' + bits0)) + sgn(boolvar ' + bits0) = boolvar ' + bits0, ¬ boolvar ∈ sgn(boolvar ' + bits0) ∧ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ #(boolvar ' + bits) = (# bits)+1
Proof step 14:
(# bits0)+1 = #(mklist(boolvar, n) + sgn(boolvar ' + bits0)), boolvar ' + bits0 = mklist(boolvar, n) + sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ 1 + # bits0 ⊦ mklist(boolvar, 1 + # bits0 - # sgn(boolvar ' + bits0)) + sgn(boolvar ' + bits0) = boolvar ' + bits0, ¬ boolvar ∈ sgn(boolvar ' + bits0) ∧ n = 0

Rule argument

seq: ⊦ #(boolvar ' + bits) = (# bits)+1 subst: [bits, boolvar] → [bits0, boolvar] rotate: F spec: list inst: bitlista name: len-05

Additional information

Used terms: bits0, boolvar