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Proof step 21 from proof add-ones-grlen (previous step)

# bits3 = # bits4 + n, # bits4 ≤ # bits3, ∀ bits0, bits, n. # bits0 < #(bits4 + boolvar0 ') → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bitsand(true ' + bits3, true ' + bits4) = true ' + mklist(true, n) + bits4, false ∈ bits3

User applied rule apply induction

And closed the goal!

Rule argument

subst: [bits0, bits, n] → [bits4, true ' + bits3, n]

Additional information

Used simplifier rules: ⊦ ¬ bits + bits0 ≠ [] ↔ bits = [] ∧ bits0 = [];% ⊦ boolvar ' ≠ [];%⊦ ¬ boolvar ∈ bits → (boolvar ∈ boolvar0 ' + bits ↔ boolvar ↔ boolvar0);% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ # boolvar ' = 0 +1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ ¬ n < n;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bits4, true ' + bits3, n