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Proof step 26 from proof bitsand-cast-04 (previous step)

# bits = 1 + # bits1, # bits1 ≤ (# bits2 + # bits) + n0, # bits1 < # bits2 + # bits ⊦ # bits1 = # bits2 + # bits, n0 = 0, sgn(bitsand(mklist(boolvar, n0) + boolvar ' + bits2 + bits, false ' + bits1)) = sgn(bitsand(boolvar ' + bits2 + bits, false ' + bits1)), bits2 + bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: bitsand-app-false rotate: F subst: [bits1, bits0, bits] → [false ' + bits1, bits2 + bits, boolvar ']

Additional information

Used simplifier rules: bitsand-app-false: ⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ ¬ bits1.first → bitsand(bits + bits0, bits1) = bitsand(bits0, bits1);% ⊦ boolvar ' + bits ≠ [];% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ m + n = n + m;% ⊦ m ≠ n → (¬ m < n ↔ n < m);% ⊦ m < n → ¬ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];% ⊦ (boolvar ' + bits).first ↔ boolvar; Used terms: false ' + bits1, bits2 + bits, boolvar '