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Proof step 77 from proof termination-RED1 (previous step)

〈RED1(t3; tn1)〉 tn1 = none, 〈RED1(t2; tn)〉 tn = tn2, ∀ t0. #(t0) < #(t3 _ t4 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), tn2 ≠ none, t3 ≠ K, #(tn2) < #(t2), value(t3 _ t4), ¬ hasS(tn2), ¬ hasS(t4), ¬ hasS(t3), ¬ value(t3), ¬ hasS(t2), ¬ (¬ hasS(t3 _ t4 _ tn2 .t) ∧ #(tn2 .t) < #(t2)), ¬ (ap(t3) ∧ ap(t3 .1) ∧ t3 .1 .1 = S), ¬ (ap(t3) ∧ t3 .1 = K ∧ value(t3 .2) ∧ value(t4)), ¬ (ap(t3) ∧ t3 .1 = S) ⊦

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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] → [tn2, t] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ some(t) ≠ none], [CSIMPSEQ : ⊦ #(some(t)) = #(t)], [CSIMPSEQ : ⊦ hasS(some(t)) ↔ hasS(t)], [CSIMPSEQ : ⊦ hasS(t _ t0) ↔ hasS(t) ∨ hasS(t0)], [CSIMPELIM : ⊦ tn ≠ none → (t = tn .t ↔ tn = some(t))])], [EXTRATERMS : (tn2, t)]]