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Proof step 32 from proof not-value-02 (previous step)

t2 .1 = S, value(t2 .2), value(C0[S _ t _ t0 _ t1]), ap(t2), ∀ t, t0, t1. ¬ value(C0[S _ t _ t0 _ t1]) ⊦ t2 = K, t2 = S

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
t2 = t3 _ t4, t3 = S, value(t4), value(C0[S _ t _ t0 _ t1]), ap(t2), ∀ t, t0, t1. ¬ value(C0[S _ t _ t0 _ t1]) ⊦ t2 = K, t2 = S

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] → [t2, t3, t4] 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 : (t2, t3, t4)]]