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Proof step 623 from proof bitsand-cast (previous step)

sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits3 ≤ m, bits3.first ⊦ bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = [], bits1 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 624:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 625:
# bits3 ≤ # mklist(false, m) ∧ bits3 ≠ [] ∧ bits3.first, sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bits3 ≤ m, bits3.first ⊦ bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = [], bits1 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, (bits2 + bitsand(mklist(false, m), bits3)) + bitsand(false ' + true ' + bits, bits1)))

Rule argument

name: bitsand-app-true rotate: F subst: [bits1, bits0, bits] → [bits3, mklist(false, m), bits2]

Additional information

Used simplifier rules: ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false); Used terms: bits3, mklist(false, m), bits2