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Proof step 20 from proof bitsand-cast-04 (previous step)

# bits1 = # bits0 ⊦ sgn(bitsand(mklist(boolvar, n0) + boolvar ' + bits0, false ' + bits1)) = sgn(bitsand(boolvar ' + bits0, false ' + bits1)), n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ ¬ bits1.first → bitsand(bits + bits0, bits1) = bitsand(bits0, bits1)

Rule argument

name: bitsand-app-false rotate: F subst: [bits1, bits0, bits] → [false ' + bits1, boolvar ' + bits0, mklist(boolvar, n0)]

Additional information

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