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Proof step 808 from proof bitsand-cast (previous step)

sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bitsand(bits0, mklist(false, # bits0)) + # bits1 < 2 + # bits + # bits0, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(bits0, mklist(false, # bits0)) + # bits1 ⊦ bits0 = [], (bits4 + bits0) + bits1 = [], bits4 + bits0 = [], bits2 + mklist(false, # bits0) = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, bitsand(bits2, bits4) + bitsand(bits0, mklist(false, # bits0)) + bitsand(bits1, false ' + true ' + bits)), bits2 = [], bits4 = [], bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: bitsand-len-false rotate: F subst: [bits0, bits] → [mklist(false, # bits0), bits0]

Additional information

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