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Proof step 12 from proof succ-fill (previous step)

false ∈ bits0 ⊦ mklist(boolvar, n0) + bits0 +1 = fillsgn(n0 + # bits0, boolvar ' + bits0 +1), n0 = 0, n0 = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ # bits < n → fillsgn(n, boolvar ' + bits) = mklist(boolvar, n - # bits) + bits

Rule argument

name: fillsgn-fill rotate: F subst: [bits, boolvar, n] → [bits0 +1, boolvar, n0 + # bits0]

Additional information

Used simplifier rules: succ-len: ⊦ false ∈ bits → # bits +1 = # bits;%succ-len: ⊦ false ∈ bits → # bits +1 = # bits;% ⊦ m + n ≤ m ↔ n = 0;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m + n - m = n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits0 +1, boolvar, n0 + # bits0