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Proof step 15 from proof value-context (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ t1 ≠ K ∧ t1 ≠ S → (value(t1 _ t2) ↔ ¬ ¬ (ap(t1) ∧ t1 .1 = S ∧ value(t2) ∧ value(t1 .2)))
Proof step 10:
¬ (C0[t] ≠ K ∧ C0[t] ≠ S), context(C0), value(C0[t] _ t0), ∀ t1. value(C0[t1]) → value(t1) ⊦ value(t)
Proof step 14:
C0[t] ≠ K ∧ C0[t] ≠ S, context(C0), ap(C0[t]) ∧ C0[t] .1 = S ∧ value(t0) ∧ value(C0[t] .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] → [t0, C0[t]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 1)) dummy: () ]

Additional information

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