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Proof step 8 from proof fill-rec (previous step)

⊦ fillsgn((n + # bits0) + 1, boolvar ' + bits0) = boolvar ' + mklist(boolvar, n) + bits0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ # bits < n → fillsgn(n, boolvar ' + bits) = mklist(boolvar, n - # bits) + bits

Rule argument

name: fillsgn-fill rotate: F subst: [bits, boolvar, n] → [bits0, boolvar, (n + # bits0) + 1]

Additional information

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