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Proof step 143 from proof bitsand-cast (previous step)

sgn(mklist(true, m) + true ' + false ' + bits1) = true ' + false ' + bits1, n = # fillsgn(n, mklist(true, m) + true ' + false ' + bits1), # bits = 2 + # bits1, n = # fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)), 2 + # bits1 + m < # fillsgn(m, bits2) + # bits, 2 + # bits1 + m < n, # bits2 < m, bits2.first, n < # fillsgn(m, bits2) + # bits, 3 + # bits1 + m < # fillsgn(m, bits2) + # bits ⊦ n = # fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1)), fillsgn(n, bits2 + bitsand(bits, true ' + false ' + bits1)) = lastn(n, fillsgn(n, fillsgn(m, bits2) + bitsand(bits, true ' + false ' + bits1))), bits2 + bits = [], bits = [], bits2 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits ≤ n → # fillsgn(n, bits) = n subst: [bits, n] → [bits2, m] rotate: F spec: bitopsaux inst: name: fill-length

Additional information

Used simplifier rules: ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;%⊦ # bits ≤ n ∧ bits ≠ [] → fillsgn(n, bits) = mklist(bits.first, n - # bits) + bits;% ⊦ m < n → m ≤ n;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0;% ⊦ m +1 = m + 1; Used terms: bits2, m