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Proof step 29 from proof value-context (previous step)

context(C0), value(t0), value(t0 _ C0[t]), ∀ t1. value(C0[t1]) → value(t1) ⊦ value(t)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ t1 ≠ K ∧ t1 ≠ S → (value(t1 _ t2) ↔ ¬ ¬ (ap(t1) ∧ t1 .1 = S ∧ value(t2) ∧ value(t1 .2)))
Proof step 24:
¬ (t0 ≠ K ∧ t0 ≠ S), context(C0), value(t0), value(t0 _ C0[t]), ∀ t1. value(C0[t1]) → value(t1) ⊦ value(t)
Proof step 28:
t0 ≠ K ∧ t0 ≠ S, context(C0), value(t0), ap(t0) ∧ t0 .1 = S ∧ value(C0[t]) ∧ value(t0 .2), ∀ t1. value(C0[t1]) → value(t1) ⊦ value(t)

Rule argument

[x0lemmaarg: spec-name: value instance-name: lemma-name: val-other-ap antecedent: succedent: t1 ≠ K ∧ t1 ≠ S → ( value(t1 _ t2) ↔ ¬ ¬ (ap(t1) ∧ t1 .1 = S ∧ value(t2) ∧ value(t1 .2))) substlist: [t2, t1] → [C0[t], t0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (C0[t], t0)]]