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Proof step 20 from proof RED-correct (previous step)

〈RED(t3; t0): kappa0 〉 t0 = t1, 〈RED1(t; tn0)〉 tn0 = some(t3), 〈RED1(t; tn0): kappa0 〉 tn0 = some(t3), ∀ t0, t2. ¬ 〈RED(t0; t'): kappa0 〉 t' = t2 ∨ t0 =>* t2 ∧ irred(t2), t => t3, ¬ t =>* t1 ∨ ¬ irred(t1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ irred(t) ↔ ¬ (∃ t'. t => t')
Proof step 19:
∀ t0, t2. ¬ 〈RED(t0; t'): kappa0 〉 t' = t2 ∨ t0 =>* t2 ∧ irred(t2), 〈RED1(t; tn0): kappa0 〉 tn0 = some(t3), 〈RED1(t; tn0)〉 tn0 = some(t3), 〈RED(t3; t0): kappa0 〉 t0 = t1, t => t3, ¬ t =>* t1 ∨ ¬ ¬ (∃ t'. t1 => t') ⊦

Rule argument

[x0lemmaarg: spec-name: reduce instance-name: lemma-name: irred-def antecedent: succedent: irred(t) ↔ ¬ (∃ t'. t => t') substlist: [t] → [t1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 5, 1, 1, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t1)]]