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Proof step 234 from proof bitsand-cast (previous step)

n0 + # bits = # fillsgn(n0 + # bits, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, # bits2 < m, 2 + # bits1 + m < n0 + # bits ⊦ mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, bitsand(mklist(false, m), bits2) + bitsand(bits, false ' + true ' + bits1)), bits2 + bits = [], bits2 = [], bits = [], bits2.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 235:
⊦ ¬ true ∈ bits ∧ (# bits0 < # bits ∧ ¬ bits0.first) ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = mklist(false, # bits0)
Proof step 236:
¬ true ∈ mklist(false, m) ∧ # bits2 < # mklist(false, m) ∧ ¬ bits2.first ∧ mklist(false, m) ≠ [] ∧ bits2 ≠ [], n0 + # bits = # fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), sgn(mklist(false, m) + false ' + true ' + bits1) = false ' + true ' + bits1, 2 + # bits1 = # bits, # bits2 < m, 2 + # bits1 + m < n0 + # bits ⊦ mklist(false, n0) + bitsand(bits, false ' + true ' + bits1) = fillsgn(n0 + # bits, mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1)), bits2 + bits = [], bits2 = [], bits = [], bits2.first

Rule argument

name: bitsand-zeros-01 rotate: F subst: [bits0, bits] → [bits2, mklist(false, m)]

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ true ∈ mklist(false, n);% ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ m < n → n ≠ 0; Used terms: bits2, mklist(false, m)