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Proof step 9 from proof value-context (previous step)

value(C0[t] _ t0), context(C0), ∀ t1. value(C0[t1]) → value(t1) ⊦ value(t), C0[t] ≠ K ∧ C0[t] ≠ S

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 4:
⊦ S = C[t] ↔ t = S ∧ C = O
Proof step 5:
⊦ O[t] = t
Proof step 6:
⊦ K = C[t] ↔ t = K ∧ C = O
Proof step 7:
⊦ S = C[t] ↔ t = S ∧ C = O
Proof step 8:
⊦ O[t] = t

Rule argument

[fma-arg: C0[t] = S]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ value(S)], [CSIMPSEQ : ⊦ value(S _ t) ↔ value(t)], [CSIMPSEQ : ⊦ K ≠ S], [CSIMPSEQ : ⊦ context(O)], [CSIMPSEQ : ⊦ value(K _ t) ↔ value(t)], [CSIMPSEQ : ⊦ value(K)])], [EXTRAFMAS : (C0[t] = S)]]