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Proof step 9 from proof fun-reduces-imp-app-reduces (previous step)

t = C[K _ v _ v0] ∧ t' = C[v] ∧ value(v) ∧ value(v0) ∧ context(C) ∨ t = C[S _ v1 _ v2 _ v3] ∧ t' = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C) ⊦ ∃ C. (∃ v1, v2. t _ t1 = C[K _ v1 _ v2] ∧ t' _ t1 = C[v1] ∧ value(v1) ∧ value(v2) ∧ context(C)) ∨ (∃ v1, v2, v3. t _ t1 = C[S _ v1 _ v2 _ v3] ∧ t' _ t1 = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C))

User applied rule exists right

And obtained the following new goals

Proof step 8:
t = C[K _ v _ v0] ∧ t' = C[v] ∧ value(v) ∧ value(v0) ∧ context(C) ∨ t = C[S _ v1 _ v2 _ v3] ∧ t' = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C) ⊦ (∃ v1, v2. t _ t1 = (C _ t1)[K _ v1 _ v2] ∧ t' _ t1 = (C _ t1)[v1] ∧ value(v1) ∧ value(v2) ∧ context(C _ t1)) ∨ (∃ v1, v2, v3. t _ t1 = (C _ t1)[S _ v1 _ v2 _ v3] ∧ t' _ t1 = (C _ t1)[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C _ t1))

Rule argument

[EXRARG : pos: right 1, [extquanttermlist: (C _ t1)abort:F, discard:T, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (C _ t1)]]