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Proof step 29 from proof RED1-lem (previous step)

〈TOPRED(t; tn)〉 tn = none, ∀ t0. #(t0) < #(t) → (true → 〈RED1(t0; tn)〉 (tn = none ⊃ irred(t0); t0 => tn .t)), ap(t), ∀ t0. ¬ t =>top t0 ⊦ 〈RED1(t .1; tn1)〉〈if tn1 ≠ none then tn1 := some(tn1 .t _ t .2) else if value(t .1) then { RED1(t .2; tn1) ; if tn1 ≠ none then tn1 := some(t .1 _ tn1 .t) }〉 (tn1 = none ⊃ irred(t); t => tn1 .t)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
〈TOPRED(t; tn)〉 tn = none, ∀ t0. #(t0) < #(t) → (true → 〈RED1(t0; tn)〉 (tn = none ⊃ irred(t0); t0 => tn .t)), ap(t), ∀ t0. ¬ t =>top t0, t = t1 _ t2 ⊦ 〈RED1(t1; tn1)〉〈if tn1 ≠ none then tn1 := some(tn1 .t _ t2) else if value(t1) then { RED1(t2; tn1) ; if tn1 ≠ none then tn1 := some(t1 _ tn1 .t) }〉 (tn1 = none ⊃ irred(t); t => tn1 .t)

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] → [t, t1, t2] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ ap(t) → ( t0 = t .1 ∧ t1 = t .2 ↔ t = t0 _ t1)])], [EXTRATERMS : (t, t1, t2)]]