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Proof step 35 from proof RED-complete (previous step)

∀ n0, t', t. n0 < n → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t'), (=> ^ n)(t, t') ⊦ 〈RED(t; t0)〉 t0 = t'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ n ≠ 0 → ((R ^ n)(t, t') ↔ (∃ t1. R(t, t1) ∧ (R ^ n -1)(t1, t')))
Proof step 13:
∀ n0, t', t. n0 < n → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t'), (=> ^ n)(t, t'), n = 0 ⊦ 〈RED(t; t0)〉 t0 = t'
Proof step 34:
∀ n0, t', t. n0 < n → (irred(t') ∧ (=> ^ n0)(t, t') → 〈RED(t; t0)〉 t0 = t'), irred(t'), ∃ t1. t => t1 ∧ (=> ^ n -1)(t1, t'), n ≠ 0 ⊦ 〈RED(t; t0)〉 t0 = t'

Rule argument

[x0lemmaarg: spec-name: reduce instance-name: lemma-name: it-rec-01 antecedent: succedent: n ≠ 0 → ((R ^ n)(t, t') ↔ (∃ t1. R(t, t1) ∧ (R ^ n -1)(t1, t'))) substlist: [t', t, n, R] → [t', t, n, =>] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t', t, n, =>)]]