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Proof step 31 from proof irred-top-01 (previous step)

irred(t1), t1 _ t2 => t' ⊦ value(t1), ∃ v1, v2, v3. t1 _ t2 = S _ v1 _ v2 _ v3 ∧ t' = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∃ v2. t1 _ t2 = K _ t' _ v2 ∧ value(t') ∧ value(v2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ irred(t) ↔ ¬ (∃ t'. t => t')
Proof step 30:
∀ t'. ¬ t1 => t', t1 _ t2 => t' ⊦ value(t1), ∃ v1, v2, v3. t1 _ t2 = S _ v1 _ v2 _ v3 ∧ t' = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∃ v2. t1 _ t2 = K _ t' _ v2 ∧ value(t') ∧ value(v2)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: irred-def antecedent: succedent: irred(t) ↔ ¬ (∃ t'. t => t') substlist: [t] → [t1] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t1)]]