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Proof step 13 from proof reduce-unique (previous step)

C[t3] = C0[K _ v _ v0], value(v), value(v0), context(C0), context(C), t3 =>top t0 ⊦ C[t0] = C0[v]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ t =>top t' ↔ (∃ v1, v2. t = K _ v1 _ v2 ∧ t' = v1 ∧ value(v1) ∧ value(v2)) ∨ (∃ v1, v2, v3. t = S _ v1 _ v2 _ v3 ∧ t' = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3))
Proof step 12:
C[t3] = C0[K _ v _ v0], value(v), value(v0), context(C0), context(C), (∃ v1, v2. t3 = K _ v1 _ v2 ∧ t0 = v1 ∧ value(v1) ∧ value(v2)) ∨ (∃ v1, v2, v3. t3 = S _ v1 _ v2 _ v3 ∧ t0 = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)) ⊦ C[t0] = C0[v]

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: topred-def antecedent: succedent: t =>top t' ↔ (∃ v1, v2. t = K _ v1 _ v2 ∧ t' = v1 ∧ value(v1) ∧ value(v2)) ∨ (∃ v1, v2, v3. t = S _ v1 _ v2 _ v3 ∧ t' = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)) substlist: [t', t] → [t0, t3] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 5)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t0, t3)]]