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Proof step 30 from proof subst-KK-equal (previous step)

∀ v1, v2, C0, v, v0. C1[K _ v1 _ v2] = C0[K _ v _ v0] ∧ value(v1) ∧ value(v2) ∧ value(v) ∧ value(v0) ∧ context(C0) ∧ context(C1) → C1[v1] = C0[v], (C1 _ t)[K _ v1 _ v2] = C0[K _ v _ v0], value(v1), value(v2), value(v), value(v0), context(C0), context(C1 _ t) ⊦ (C1 _ t)[v1] = C0[v]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
⊦ (C _ t1)[t] = C[t] _ t1
Proof step 29:
C1[K _ v1 _ v2] _ t = C0[K _ v _ v0], value(v1), value(v2), value(v), value(v0), context(C0), context(C1), ∀ v3, v4, C, v5, v6. C1[K _ v3 _ v4] = C[K _ v5 _ v6] ∧ value(v3) ∧ value(v4) ∧ value(v5) ∧ value(v6) ∧ context(C) → C1[v3] = C[v5] ⊦ C1[v1] _ t = C0[v]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ context(C _ t) ↔ context(C)])]]