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Proof step 579 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, true ' + false ' + bits), # bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + # bits0 = # bitsand(mklist(true, # bits0), bits0) + # bits1, mklist(true, # bits0).first ⊦ bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = [], bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], bits0 = bitsand(mklist(true, # bits0), bits0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 580:
⊦ ¬ false ∈ bits ∧ # bits0 ≤ # bits ∧ bits0.first ∧ bits0 ≠ [] → bitsand(bits, bits0) = fillsgn(# bits, bits0)
Proof step 581:
¬(¬ false ∈ mklist(true, # bits0) ∧ # bits0 ≤ # mklist(true, # bits0) ∧ bits0.first ∧ bits0 ≠ []), # bits1 = # bitsand(bits1, true ' + false ' + bits), # bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, 2 + # bits + # bits0 = # bitsand(mklist(true, # bits0), bits0) + # bits1, mklist(true, # bits0).first ⊦ bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = [], bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], bits0 = bitsand(mklist(true, # bits0), bits0)

Rule argument

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

Additional information

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