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Proof step 486 from proof bitsand-cast (previous step)

sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first ⊦ bits4 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits))), bits4 + bits0 = [], bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 487:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 488:
¬(¬ false ∈ mklist(true, # bits0) ∧ # bits0 ≤ # mklist(true, # bits0) ∧ bits0.first ∧ bits0 ≠ []), sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first ⊦ bits4 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits))), bits4 + bits0 = [], bits0 = []

Rule argument

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

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ fillsgn(# bits, bits) = bits; Used terms: bits0, mklist(true, # bits0)