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Proof step 57 from proof reduction-is-topred-in-ctxt (previous step)

context(C0), t2 = K _ v _ v0 ∧ t = v ∧ value(v) ∧ value(v0) ∨ t2 = S _ v1 _ v2 _ v3 ∧ t = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∀ t'. v4 => t' ↔ (∃ C, t0, t2. context(C) ∧ v4 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]), ∀ t'. C0[t2] => t' ↔ (∃ C, t, t1. context(C) ∧ C0[t2] = C[t] ∧ t =>top t1 ∧ t' = C[t1]) ⊦ C0[t2] _ v4 => C0[t] _ v4

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: one-step-red-def antecedent: succedent: t => t' ↔ (∃ C. (∃ v1, v2. t = C[K _ v1 _ v2] ∧ t' = C[v1] ∧ value(v1) ∧ value(v2) ∧ context(C)) ∨ (∃ v1, v2, v3. t = C[S _ v1 _ v2 _ v3] ∧ t' = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C))) substlist: [t', t] → [C0[t] _ v4, C0[t2] _ v4] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (C0[t] _ v4, C0[t2] _ v4)]]