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Proof step 15 from proof fill-sgn-01 (previous step)

¬ #(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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
n1 + # bits0 = n + # sgn(boolvar ' + bits0), # sgn(boolvar ' + bits0) ≤ n1 + # bits0, # sgn(boolvar ' + bits0) ≤ 1 + # 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

Additional information

Used simplifier rules: ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;