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Proof step 25 from proof irred-top (previous step)

context(C0), value(v3), value(v2), value(v1), value(v5), ∀ t'. ¬ C0[S _ v1 _ v2 _ v3] => t', ∀ t'. ¬ v5 => t' ⊦ ∃ v. v5 _ C0[S _ v1 _ v2 _ v3] = K _ (v5 _ C0[v1 _ v3 _ (v2 _ v3)]) _ v ∧ value(v5 _ C0[v1 _ v3 _ (v2 _ v3)]) ∧ value(v), ∃ v, v0, v4. v5 _ C0[S _ v1 _ v2 _ v3] = S _ v _ v0 _ v4 ∧ v5 _ C0[v1 _ v3 _ (v2 _ v3)] = v _ v4 _ (v0 _ v4) ∧ value(v) ∧ value(v0) ∧ value(v4)

User applied rule all left

And obtained the following new goals

Proof step 24:
context(C0), value(v3), value(v2), value(v1), value(v5), ¬ C0[S _ v1 _ v2 _ v3] => C0[v1 _ v3 _ (v2 _ v3)], ∀ t'. ¬ v5 => t' ⊦ ∃ v. v5 _ C0[S _ v1 _ v2 _ v3] = K _ (v5 _ C0[v1 _ v3 _ (v2 _ v3)]) _ v ∧ value(v5 _ C0[v1 _ v3 _ (v2 _ v3)]) ∧ value(v), ∃ v, v0, v4. v5 _ C0[S _ v1 _ v2 _ v3] = S _ v _ v0 _ v4 ∧ v5 _ C0[v1 _ v3 _ (v2 _ v3)] = v _ v4 _ (v0 _ v4) ∧ value(v) ∧ value(v0) ∧ value(v4)

Rule argument

[EXRARG : pos: left 6, [extquanttermlist: (C0[v1 _ v3 _ (v2 _ v3)]) abort:F , discard:T , computed:F ]]

Additional information

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