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Proof step 12 from proof ls-ext (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
⊦ m ' + nx < n ↔ m < n ∧ nx < n
Proof step 14:
m0 < m, ∀ n. n ∈ nx0 → n < m, ∀ m. nx0 < m ↔ (∀ n. n ∈ nx0 → n < m) ⊦ nx0 < m

Rule argument

Additional information

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