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Proof step 71 from proof reduction-is-topred-in-ctxt (previous step)

t0 _ t1 = C[t2], context(C), t2 =>top t, ∀ t'. t0 => t' ↔ (∃ C, t2, t1. context(C) ∧ t0 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]), ∀ t'. t1 => t' ↔ (∃ C, t0, t2. context(C) ∧ t1 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]) ⊦ t0 _ t1 => C[t]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ 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 70:
t0 _ t1 = C[t2], context(C), (∃ v1, v2. t2 = K _ v1 _ v2 ∧ t = v1 ∧ value(v1) ∧ value(v2)) ∨ (∃ v1, v2, v3. t2 = S _ v1 _ v2 _ v3 ∧ t = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)), ∀ t'. t0 => t' ↔ (∃ C, t2, t1. context(C) ∧ t0 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]), ∀ t'. t1 => t' ↔ (∃ C, t0, t2. context(C) ∧ t1 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]) ⊦ t0 _ t1 => C[t]

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] → [t, t2] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t, t2)]]