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Proof step 18 from proof reduction-is-topred-in-ctxt (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
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]) ⊦ ∃ C, t2, t3. context(C) ∧ S _ v1 _ v2 _ v3 = C[t2] ∧ t2 =>top t3 ∧ v1 _ v3 _ (v2 _ v3) = C[t3]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ t _ t0 = t1 _ t2 ↔ t = t1 ∧ t0 = t2])]]