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Proof step 166 from proof kappa-RED1 (previous step)

〈RED1(t; tn2)〉 tn2 = tn0, 〈RED1(t .1; tn3): m 〉 tn3 = none, 〈TOPRED(t; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ none, ap(t), ¬ value(t .1) ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 165:
〈RED1(t; tn2)〉 tn2 = tn0, 〈RED1(t0; tn3): m 〉 tn3 = none, 〈TOPRED(t; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ none, ap(t), ¬ value(t0), t = t0 _ t1 ⊦

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] → [t, t0, t1] 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 : (t, t0, t1)]]