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Proof step 20 from proof not-value-02 (previous step)

value(C0[S _ t _ t0 _ t1] _ t2), ∀ t, t0, t1. ¬ value(C0[S _ t _ t0 _ t1]) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ t1 ≠ K ∧ t1 ≠ S → (value(t1 _ t2) ↔ ¬ ¬ (ap(t1) ∧ t1 .1 = S ∧ value(t2) ∧ value(t1 .2)))
Proof step 7:
⊦ C[t _ t0] ≠ K
Proof step 8:
⊦ C[t _ t0] ≠ S
Proof step 19:
C0[S _ t _ t0 _ t1] ≠ K ∧ C0[S _ t _ t0 _ t1] ≠ S, ap(C0[S _ t _ t0 _ t1]) ∧ C0[S _ t _ t0 _ t1] .1 = S ∧ value(t2) ∧ value(C0[S _ t _ t0 _ t1] .2), ∀ t, t0, t1. ¬ value(C0[S _ t _ t0 _ t1]) ⊦

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] → [t2, C0[S _ t _ t0 _ t1]] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t2, C0[S _ t _ t0 _ t1])]]