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Proof step 7 from proof bitsor-ones-samelen (previous step)

# bits = 1 + # bits1 ⊦ bits = [], bitsor(bits, true ' + bits1) = bits, false ∈ bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ¬ false ∈ bits ∧ bits0.first ∧ # bits ≤ # bits0 ∧ bits ≠ [] ∧ bits0 ≠ [] → bitsor(bits, bits0) = bits

Rule argument

name: bitsor-ones-true rotate: F subst: [bits0, bits] → [true ' + bits1, bits]

Additional information

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