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

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

Rule argument

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

Additional information

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