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Proof step 11 from proof termination-RED (previous step)

∀ t0. #(t0) < #(t) → (¬ hasS(t0) → 〈RED(t0; t')〉 true), ¬ hasS(t) ⊦ 〈RED1(t; tn0)〉〈if tn0 ≠ none then RED(tn0 .t; t0) else t0 := t〉 true

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
¬ hasS(t) ⊦ 〈RED1(t; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t))
Proof step 10:
〈RED1(t; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t)), ∀ t0. #(t0) < #(t) → (¬ hasS(t0) → 〈RED(t0; t')〉 true), ¬ hasS(t) ⊦ 〈RED1(t; tn0)〉〈if tn0 ≠ none then RED(tn0 .t; t0) else t0 := t〉 true

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: termination-RED1 antecedent: ¬ hasS(t) succedent: 〈RED1(t; tn)〉 (tn ≠ none → #(tn) < #(t)) substlist: [t] → [t] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t)]]