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Proof step 51 from proof kappa-RED1 (previous step)

〈RED1(t0 _ t1; tn2)〉 tn2 = tn0, 〈RED1(t0; tn3): m 〉 tn3 = tn4, 〈TOPRED(t0 _ t1; 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 ≠ some(tn4 .t _ t1), tn4 ≠ none ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 50:
〈RED1(t0 _ t1; tn2)〉 tn2 = tn0, 〈RED1(t0; tn3): m 〉 tn3 = tn4, 〈TOPRED(t0 _ t1; 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 ≠ some(t2 _ t1), tn4 ≠ none, tn4 = some(t2) ⊦

Rule argument

[x0lemmaarg: spec-name: term_or_none instance-name: lemma-name: elim antecedent: succedent: tn ≠ none → (t = tn .t ↔ tn = some(t)) substlist: [tn, t] → [tn4, t2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ tn ≠ none → (t = tn .t ↔ tn = some(t))])], [EXTRATERMS : (tn4, t2)]]