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Proof step 223 from proof bitsand-cast (previous step)

n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, 2 + # bits1 + m < n ⊦ fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits2 + bits = [], bits2 = [], m = 0, bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits subst: [bits, n] → [bitsand(bits, false ' + true ' + bits1), n] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: and-notempty-01: ⊦ bits ≠ [] → bitsand(bits, boolvar ' + bits0) ≠ [];% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ ¬ # fillsgn(n, bits) < # bits; Used terms: bitsand(bits, false ' + true ' + bits1), n