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

⊦ n0 = 0, ((¬ boolvar)' + mklist(¬ boolvar, n0)) + bitsinvert(bits0) = fillsgn((1 + # bits0) + n0, (¬ boolvar)' + bitsinvert(bits0))

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] → [bitsinvert(bits0), ¬ boolvar, (1 + # bits0) + n0]

Additional information

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