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Proof step 47 from proof reduction-is-topred-in-ctxt (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 45:
⊦ value(v) ∧ value(v0) → K _ v _ v0 => v
Proof step 46:
⊦ value(v1) ∧ value(v2) ∧ value(v3) → S _ v1 _ v2 _ v3 => v1 _ v3 _ (v2 _ v3)

Rule argument

[CASEDARG : pos: left 1, ()]

Additional information

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