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Proof step 12 from proof irred-top (previous step)

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

User applied rule all left

And obtained the following new goals

Proof step 11:
context(C0), value(v0), value(v), value(v4), ¬ C0[K _ v _ v0] => C0[v], ∀ t'. ¬ v4 => t' ⊦ ∃ v1. v4 _ C0[K _ v _ v0] = K _ (v4 _ C0[v]) _ v1 ∧ value(v4 _ C0[v]) ∧ value(v1), ∃ v1, v2, v3. v4 _ C0[K _ v _ v0] = S _ v1 _ v2 _ v3 ∧ v4 _ C0[v] = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3)

Rule argument

[EXRARG : pos: left 5, [extquanttermlist: (C0[v])abort:F, discard:T, computed:F]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (C0[v])]]