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Proof step 13 from proof value-context (previous step)

C0[t] .1 = S, value(C0[t] .2), value(t0), ap(C0[t]), context(C0), ∀ t1. value(C0[t1]) → value(t1) ⊦ C0[t] = K, C0[t] = S, value(t)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
C0[t] = t2 _ t3, t2 = S, value(t3), value(t0), ap(C0[t]), context(C0), ∀ t1. value(C0[t1]) → value(t1) ⊦ C0[t] = K, C0[t] = S, value(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] → [C0[t], t2, t3] 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 : (C0[t], t2, t3)]]