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Proof step 7 from proof le-add-bound (previous step)

n ≤ m, ∀ n0. n0 ∈ ns → n0 < n ⊦ ∀ n0. n0 ∈ ns → n0 < m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n0 ∈ ns, n ≤ n0, m ≤ n0, n ≤ m, ∀ n0. n0 ∈ ns → n0 < n ⊦ # ns = 0, ns = ∅

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ns ≠ ∅ → # ns ≠ 0; (forward) from specification set-basic[nat-set]%ne-01: ⊦ n ∈ ns → ns ≠ ∅; (forward) from specification set-basic[nat-set]%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)