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Proof step 13 from proof fill-sgn-01 (previous step)

n1 + # bits0 = n + # sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ n1 + # bits0, ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ n1 = 0, mklist(boolvar, n) + sgn(boolvar ' + bits0) = mklist(boolvar, n1) + bits0

User applied rule insert lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ # bits < # sgn(bits)
Proof step 15:
¬ #(boolvar ' + bits0) < # sgn(boolvar ' + bits0), n1 + # bits0 = n + # sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ n1 + # bits0, ∀ n0. ¬ n0 < # bits0 → fillsgn(n0, sgn(bits0)) = fillsgn(n0, bits0) ⊦ n1 = 0, mklist(boolvar, n) + sgn(boolvar ' + bits0) = mklist(boolvar, n1) + bits0

Rule argument

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

Additional information

Used terms: boolvar ' + bits0