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Proof step 415 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 416:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 417:
# bits3 ≤ # mklist(true, m) ∧ bits3 ≠ [] ∧ bits3.first, # bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, # bits3 ≤ m, bits3.first ⊦ bits3 = [], bits2 + mklist(true, m) = [], lastn(2 + # bits + m, fillsgn(2 + # bits + m, bits3 + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, (bits2 + bitsand(mklist(true, m), bits3)) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits3 + bits1 = []

Rule argument

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

Additional information

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