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Proof step 158 from proof bitsand-cast (previous step)

sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, n0 + # bits2 + # bits = # fillsgn(n0 + # bits2 + # bits, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), 2 + # bits1 + m < n0 + # bits2 + # bits, # bits2 < m, bits2.first ⊦ mklist(true, n0) + bits2 + bitsand(bits, true ' + false ' + bits1) = fillsgn(n0 + # bits2 + # bits, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), bits2 + bits = [], bits = [], bits2 = [], bits2 + bitsand(bits, true ' + false ' + bits1) = []

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] → [bits2, m] rotate: F spec: bitopsaux inst: name: fill-fill

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: bits2, m