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Proof step 11 from proof fill-sgn (previous step)

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 cut formula

And obtained the following new goals

Proof step 12:
#(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
Proof step 16:
boolvar ' + bits0 = mklist(boolvar, n) + sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ 1 + # bits0 ⊦ #(boolvar ' + bits0) = #(mklist(boolvar, n) + sgn(boolvar ' + bits0)), mklist(boolvar, 1 + # bits0 - # sgn(boolvar ' + bits0)) + sgn(boolvar ' + bits0) = boolvar ' + bits0, ¬ boolvar ∈ sgn(boolvar ' + bits0) ∧ n = 0

Rule argument

fma: #(boolvar ' + bits0) = #(mklist(boolvar, n) + sgn(boolvar ' + bits0))

Additional information

Used formulas: #(boolvar ' + bits0) = #(mklist(boolvar, n) + sgn(boolvar ' + bits0))