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Proof step 657 from proof SII-loops (previous step)

〈RED1(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); tn0): kappa - 1 〉〈if tn0 ≠ none then RED(tn0 .t; t3): kappa - 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < kappa → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), kappa ≠ 0 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 656:
〈RED1(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); tn0): m 〉〈if tn0 ≠ none then RED(tn0 .t; t3): m else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < kappa → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), kappa ≠ 0, kappa = m + 1 ⊦

Rule argument

[x0lemmaarg: spec-name: nat instance-name: lemma-name: elim-pred-c antecedent: n ≠ 0 succedent: m = n - 1 ↔ n = m + 1 substlist: [n, m] → [kappa, m] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1])], [EXTRATERMS : (kappa, m)]]