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Proof step 37 from proof reduction-is-topred-in-ctxt (previous step)

value(v4), context(C0), value(v3), value(v2), value(v1), ∀ t'. C0[S _ v1 _ v2 _ v3] => t' ↔ (∃ C, t0, t2. context(C) ∧ C0[S _ v1 _ v2 _ v3] = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]), ∀ t'. v4 => t' ↔ (∃ C, t2, t1. context(C) ∧ v4 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]) ⊦ ∃ C, t2, t3. context(C) ∧ v4 _ C0[S _ v1 _ v2 _ v3] = C[t2] ∧ t2 =>top t3 ∧ v4 _ C0[v1 _ v3 _ (v2 _ v3)] = C[t3]

User applied rule exists right

And obtained the following new goals

Proof step 36:
value(v4), context(C0), value(v3), value(v2), value(v1), ∀ t'. C0[S _ v1 _ v2 _ v3] => t' ↔ (∃ C, t0, t2. context(C) ∧ C0[S _ v1 _ v2 _ v3] = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]), ∀ t'. v4 => t' ↔ (∃ C, t2, t1. context(C) ∧ v4 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]) ⊦ context(v4 _ C0) ∧ v4 _ C0[S _ v1 _ v2 _ v3] = (v4 _ C0)[S _ v1 _ v2 _ v3] ∧ S _ v1 _ v2 _ v3 =>top v1 _ v3 _ (v2 _ v3) ∧ v4 _ C0[v1 _ v3 _ (v2 _ v3)] = (v4 _ C0)[v1 _ v3 _ (v2 _ v3)]

Rule argument

[EXRARG : pos: right 1, [extquanttermlist: (v4 _ C0, S _ v1 _ v2 _ v3, v1 _ v3 _ (v2 _ v3)) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (v4 _ C0, S _ v1 _ v2 _ v3, v1 _ v3 _ (v2 _ v3))]]