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Proof step 2 from proof firstN-in-01 (previous step)

n < # x, a ∈ firstn(n, x) ⊦ a ∈ x

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ a ∈ x ∧ n ≤ # x → ¬ a ∈ firstn(n, x)

Rule argument

spec: <toplevel> name: firstN-in seq: ⊦ ¬ a ∈ x ∧ n ≤ # x → ¬ a ∈ firstn(n, x) subst: [x, n, a] → [x, n, a] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → ¬ n < m; (s) Used terms: x, n, a