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Proof step 5 from proof ls-prepend-bound-add1 (previous step)

nx < m ⊦ ∀ n. n ∈ m ' + nx → n < m + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
m < n, nx < m, n ∈ nx ⊦ n = m

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (nx + nx0) + nx1 = nx + nx0 + nx1; from specification list[nat-list-set]% ⊦ n ∈ n0 ' + nx ↔ n = n0 ∨ n ∈ nx; (s)