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Proof step 577 from proof SII-loops (previous step)

〈TOPRED(K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m0 - 1 〉〈if tn1 = none then { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ tn1 .t) } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))))〉〈if tn ≠ none then RED(tn .t; t3): 1 + m0 else t3 := K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t3 = t, ∀ kappa0, t. kappa0 < (((m0 + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), m0 ≠ 0 ⊦

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 576:
〈TOPRED(K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))); tn1): m 〉〈if tn1 = none then { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(tn1 .t _ (K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ tn1 .t) } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K))))〉〈if tn ≠ none then RED(tn .t; t3): 1 + m0 else t3 := K _ (S _ (S _ K _ K) _ (S _ K _ K)) _ (K _ (S _ (S _ K _ K) _ (S _ K _ K))) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t3 = t, ∀ kappa0, t. kappa0 < (((m0 + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), m0 ≠ 0, m0 = 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] → [m0, 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 : (m0, m)]]