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Proof step 278 from proof kappa-RED1 (previous step)

〈RED1(t2 _ t3 _ t1; tn3)〉 tn3 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), t2 .1 = S, tn0 ≠ some(t2 .2 _ t1 _ (t3 _ t1)), m ≠ 0, t2 ≠ K, ap(t2), value(t2 .2), value(t3), value(t1) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 277:
〈RED1(t2 _ t3 _ t1; tn3)〉 tn3 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), t0 = S, tn0 ≠ some(t4 _ t1 _ (t3 _ t1)), m ≠ 0, t2 ≠ K, ap(t2), value(t4), value(t3), value(t1), t2 = t0 _ t4 ⊦

Rule argument

[x0lemmaarg: spec-name: term instance-name: lemma-name: elim antecedent: succedent: ap(t) → (t0 = t .1 ∧ t1 = t .2 ↔ t = t0 _ t1) substlist: [t, t0, t1] → [t2, t0, t4] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ ap(t) → ( t0 = t .1 ∧ t1 = t .2 ↔ t = t0 _ t1)])], [EXTRATERMS : (t2, t0, t4)]]