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Proof step 4 from proof S-reduce (previous step)

value(v3), value(v2), value(v1) ⊦ ∃ C. (∃ v, v0. S _ v1 _ v2 _ v3 = C[K _ v _ v0] ∧ v1 _ v3 _ (v2 _ v3) = C[v] ∧ value(v) ∧ value(v0) ∧ context(C)) ∨ (∃ v, v0, v4. S _ v1 _ v2 _ v3 = C[S _ v _ v0 _ v4] ∧ v1 _ v3 _ (v2 _ v3) = C[v _ v4 _ (v0 _ v4)] ∧ value(v) ∧ value(v0) ∧ value(v4) ∧ context(C))

User applied rule exists right

And obtained the following new goals

Proof step 3:
value(v3), value(v2), value(v1) ⊦ (∃ v, v0. S _ v1 _ v2 _ v3 = O[K _ v _ v0] ∧ v1 _ v3 _ (v2 _ v3) = O[v] ∧ value(v) ∧ value(v0) ∧ context(O)) ∨ (∃ v, v0, v4. S _ v1 _ v2 _ v3 = O[S _ v _ v0 _ v4] ∧ v1 _ v3 _ (v2 _ v3) = O[v _ v4 _ (v0 _ v4)] ∧ value(v) ∧ value(v0) ∧ value(v4) ∧ context(O))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (O)]]