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Proof step 212 from proof bitsand-cast (previous step)

sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, n = # fillsgn(n, mklist(false, m) + false ' + true ' + bits1), n = # fillsgn(n, bitsand(bits, false ' + true ' + bits1)), 2 + # bits1 + m < n, n < (2 + # bits1) + # bitsand(bits2, mklist(false, m)), m + 1 < # bitsand(bits2, mklist(false, m)), m < # bitsand(bits2, mklist(false, m)) ⊦ bits2 = [], n = # fillsgn(n, bitsand(bits2, mklist(false, m)) + bitsand(bits, false ' + true ' + bits1)), bits = [], m = 0, bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(bits2, mklist(false, m)) + bitsand(bits, false ' + true ' + bits1))), bitsand(bits2, mklist(false, m)) = []

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, m), bits2]

Additional information

Used simplifier rules: and-notempty: ⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ # mklist(boolvar, n) = n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n → ¬ n < m; Used terms: mklist(false, m), bits2