[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 41 from proof termination-RED1 (previous step)

〈RED1(t4; tn2)〉 tn2 = none, 〈RED1(t5 _ t6; tn1)〉 tn1 = none, ∀ t0. #(t0) < #(t5 _ t6 _ t4 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), t5 .1 = S, t5 ≠ S, t5 ≠ K, value(t5 _ t6 _ t4), ap(t5), value(t6), value(t5 .2), ¬ hasS(t4), ¬ hasS(t2), ¬ hasS(t5), ¬ hasS(t6), ¬ value(t4) ⊦ 〈RED1(t2; tn0)〉 〈t1 := t5 _ t6 _ t4 ; if tn0 ≠ none then tn0 := some(t1 _ tn0 .t)〉 (tn0 ≠ none → ¬ hasS(tn0) ∧ ¬ #(t1) + #(t2) < #(tn0))

Heuristic elimination applied rule insert elim lemma

And closed the goal!

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] → [t5, t, t3] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ t _ t0 ≠ S], [CSIMPSEQ : ⊦ t _ t0 ≠ K], [CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ hasS(t _ t0) ↔ hasS(t) ∨ hasS(t0)], [CSIMPSEQ : ⊦ hasS(S)], [CSIMPELIM : ⊦ ap(t) → ( t0 = t .1 ∧ t1 = t .2 ↔ t = t0 _ t1)])], [EXTRATERMS : (t5, t, t3)]]