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Proof step 36 from proof partitions-mod-count (previous step)

partitions(pe(m, m0, m1) ' + P0, n0), ∀ n, m, m0, m1, n0, m2. P0[n] = pe(m, m0, m1) ∧ n < # P0 ∧ partitions(P0, n0) → P0 = [] ∨ partitions(P0[n, pe(m, m0, m2)], n0) ⊦ partitions(pe(m, m0, m2) ' + P0, n0)

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] → [n0, pe(m, m0, m2) ' + P0] flags:rewrite, current

Additional information

[Concretesimprules(()), Extraterms((n0pe(m, m0, m2) ' + P0))]