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Proof step 5 from proof fill-rec (previous step)

bits = boolvar + bits0, # bits ≤ m ⊦ fillsgn(m + 1, bits) = boolvar ' + fillsgn(m, bits), bits = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# bits0 < m ⊦ fillsgn(m + 1, boolvar ' + bits0) = boolvar ' + mklist(boolvar, m - # bits0) + bits0

Rule argument

Additional information

Used simplifier rules: fillsgn-fill: ⊦ # bits < n → fillsgn(n, boolvar ' + bits) = mklist(boolvar, n - # bits) + bits;% ⊦ m < n → n ≠ 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;