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Proof step 6 from proof fill-rec-false (previous step)

⊦ fillsgn(2 + # bits0 + n0, false ' + bits0) = false ' + (false ' + mklist(false, n0)) + bits0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ # bits < n → fillsgn(n, boolvar ' + bits) = mklist(boolvar, n - # bits) + bits

Rule argument

name: fillsgn-fill rotate: F subst: [bits, boolvar, n] → [bits0, false, 2 + # bits0 + n0]

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;% ⊦ m + n ≤ m ↔ n = 0;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ 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, 2) = boolvar ' + boolvar ';% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1; Used terms: bits0, false, 2 + # bits0 + n0