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Proof step 16 from proof reduction-is-topred-in-ctxt (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
value(v3), value(v2), value(v1), ∀ t'. v3 => t' ↔ (∃ C, t0, t2. context(C) ∧ v3 = C[t0] ∧ t0 =>top t2 ∧ t' = C[t2]), ∀ t'. S _ v1 _ v2 => t' ↔ (∃ C, t2, t1. context(C) ∧ S _ v1 _ v2 = C[t2] ∧ t2 =>top t1 ∧ t' = C[t1]) ⊦ S _ v1 _ v2 _ v3 =>top v1 _ v3 _ (v2 _ v3)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ O[t] = t], [CSIMPSEQ : ⊦ context(O)])]]