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Proof step 65 from proof reduction-is-topred-in-ctxt (previous step)

value(v4), context(C0), t2 = K _ v _ v0 ∧ t = v ∧ value(v) ∧ value(v0) ∨ t2 = S _ v1 _ v2 _ v3 ∧ t = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∀ t'. C0[t2] => t' ↔ (∃ C, t0, t. context(C) ∧ C0[t2] = C[t0] ∧ t0 =>top t ∧ t' = C[t]), ∀ t'. v4 => t' ↔ (∃ C, t2, t1. context(C) ∧ v4 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]) ⊦ (∃ v1, v2. v4 _ C0[t2] = (v4 _ C0)[K _ v1 _ v2] ∧ v4 _ C0[t] = (v4 _ C0)[v1] ∧ value(v1) ∧ value(v2) ∧ context(v4 _ C0)) ∨ (∃ v1, v2, v3. v4 _ C0[t2] = (v4 _ C0)[S _ v1 _ v2 _ v3] ∧ v4 _ C0[t] = (v4 _ C0)[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(v4 _ C0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
value(v4), context(C0), t2 = K _ v _ v0 ∧ t = v ∧ value(v) ∧ value(v0) ∨ t2 = S _ v1 _ v2 _ v3 ∧ t = v1 _ v3 _ (v2 _ v3) ∧ value(v1) ∧ value(v2) ∧ value(v3), ∀ t'. C0[t2] => t' ↔ (∃ C, t0, t. context(C) ∧ C0[t2] = C[t0] ∧ t0 =>top t ∧ t' = C[t]), ∀ t'. v4 => t' ↔ (∃ C, t2, t1. context(C) ∧ v4 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]) ⊦ ∃ v5, v6. v4 _ C0[t2] = v4 _ C0[K _ v5 _ v6] ∧ v4 _ C0[t] = v4 _ C0[v5] ∧ value(v5) ∧ value(v6), ∃ v5, v6, v7. v4 _ C0[t2] = v4 _ C0[S _ v5 _ v6 _ v7] ∧ v4 _ C0[t] = v4 _ C0[v5 _ v7 _ (v6 _ v7)] ∧ value(v5) ∧ value(v6) ∧ value(v7)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ context(t _ C) ↔ ¬ ¬ (context(C) ∧ value(t))], [CSIMPSEQ : ⊦ (t1 _ C)[t] = t1 _ C[t]])]]