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Proof step 218 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)), # bits2 < # bitsand(mklist(false, m), bits2), 2 + # bits1 + m < n, n < (2 + # bits1) + # bitsand(mklist(false, m), bits2), m + 1 < # bitsand(mklist(false, m), bits2), m < # bitsand(mklist(false, m), bits2), # bits2 < m, # bits2 + 1 < # bitsand(mklist(false, m), bits2) ⊦ bits2 = [], n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits = [], bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 219:
⊦ ¬ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits0
Proof step 220:
¬(¬ bits2.first ∧ # bits2 ≤ # mklist(false, m) ∧ bits2 ≠ []), 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)), # bits2 < # bitsand(mklist(false, m), bits2), 2 + # bits1 + m < n, n < (2 + # bits1) + # bitsand(mklist(false, m), bits2), m + 1 < # bitsand(mklist(false, m), bits2), m < # bitsand(mklist(false, m), bits2), # bits2 < m, # bits2 + 1 < # bitsand(mklist(false, m), bits2) ⊦ bits2 = [], n = # fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits = [], bits2 + bits = [], fillsgn(n, bitsand(bits, false ' + true ' + bits1)) = lastn(n, fillsgn(n, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)))

Rule argument

name: bitsand-len-false rotate: F subst: [bits0, bits] → [bits2, mklist(false, m)]

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ m < n → m ≤ n;% ⊦ ¬ n < n; Used terms: bits2, mklist(false, m)