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Proof step 418 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 419:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 420:
¬ false ∈ mklist(true, m) ∧ # bits3 ≤ # mklist(true, m) ∧ bits3.first ∧ bits3 ≠ [], # bits1 = 2 + # bits, sgn(mklist(true, m) + true ' + false ' + bits) = true ' + false ' + bits, bits3.first, # bits3 ≤ m ⊦ 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 + fillsgn(# mklist(true, m), bits3)) + bitsand(bits1, true ' + false ' + bits))), bits1 = [], bits3 + bits1 = [], bits3 = []

Rule argument

name: add-ones-grlen rotate: F subst: [bits0, bits] → [bits3, mklist(true, m)]

Additional information

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