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Proof step 5 from proof ls-ext (previous step)

m0 ' + nx0 < m, ∀ m. nx0 < m ↔ (∀ n. n ∈ nx0 → n < m) ⊦ m0 ' + nx0 < m ↔ (∀ n. n = m0 ∨ n ∈ nx0 → n < m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ m ' + nx < n ↔ m < n ∧ nx < n
Proof step 7:
m0 < m, nx0 < m, m0 < n, n ∈ nx0, m ≤ n, ∀ m. nx0 < m ↔ (∀ n. n ∈ nx0 → n < m) ⊦ n = m0

Rule argument

Additional information

Used simplifier rules: ls-rec: ⊦ m ' + nx < n ↔ m < n ∧ nx < n;% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]