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Proof step 32 from proof RED-correct (previous step)

〈if tn ≠ none then RED(tn .t; t0): kappa0 else t0 := t〉 t0 = t1, 〈RED1(t; tn0): kappa0 〉 tn0 = tn, ∀ t0, t2. ¬ 〈RED(t0; t'): kappa0 〉 t' = t2 ∨ t0 =>* t2 ∧ irred(t2), ¬ t =>* t1 ∨ ¬ irred(t1) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
⊦ 〈RED1(t; tn)〉 (tn = none ⊃ irred(t); t => tn .t)
Proof step 31:
〈RED1(t; tn)〉 (tn = none ⊃ irred(t); t => tn .t), 〈if tn ≠ none then RED(tn .t; t0): kappa0 else t0 := t〉 t0 = t1, 〈RED1(t; tn0): kappa0 〉 tn0 = tn, ∀ t0, t2. ¬ 〈RED(t0; t'): kappa0 〉 t' = t2 ∨ t0 =>* t2 ∧ irred(t2), ¬ t =>* t1 ∨ ¬ irred(t1) ⊦

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: RED1-lem antecedent: succedent: 〈RED1(t; tn)〉 (tn = none ⊃ ¬ (∃ t0. t => t0); t => 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)]]