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Proof step 5 from proof split-init-2 (previous step)

split([], A, X), partitions([], # A) ⊦ split([], A, [])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ partitions(P, n0) ↔ (∀ n. n < n0 → (∃ m. m < # P ∧ n ∈ P[m] ∧ (∀ m0. m0 < # P ∧ m0 ≠ m → ¬ n ∈ P[m0])))

Rule argument

spec: inst: name:partititions-def seq: ⊦ partitions(P, n0) ↔ (∀ n. n < n0 → (∃ m. m < # P ∧ n ∈ P[m] ∧ (∀ m0. m0 < # P ∧ m0 ≠ m → ¬ n ∈ P[m0]))) subst:[n0, P] → [# A, []] flags:rewrite, current

Additional information

[Concretesimprules(()), Extraterms((# A[]))]