[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 45 from proof subst-SK-equal (previous step)

t _ C1[S _ v3 _ v4 _ v5] = C0[K _ v _ v0], value(v3), value(v4), value(v5), value(v), value(v0), context(C0), context(C1), value(t), ∀ v1, v2, v6, C, v7, v8. C1[S _ v1 _ v2 _ v6] = C[K _ v7 _ v8] ∧ value(v1) ∧ value(v2) ∧ value(v6) ∧ value(v7) ∧ value(v8) ∧ context(C) → C1[v1 _ v6 _ (v2 _ v6)] = C[v7] ⊦ t _ C1[v3 _ v5 _ (v4 _ v5)] = C0[v]

User applied rule constructor cut

And obtained the following new goals

Proof step 38:
⊦ O[t] = t
Proof step 39:
⊦ ¬ value(C[S _ t _ t0 _ t1])
Proof step 40:
⊦ (C _ t1)[t] = C[t] _ t1
Proof step 41:
⊦ ¬ value(C[K _ t _ t0])
Proof step 44:
C0 = t0 _ C2, t _ C1[S _ v3 _ v4 _ v5] = C0[K _ v _ v0], value(v3), value(v4), value(v5), value(v), value(v0), context(C0), context(C1), value(t), ∀ v1, v2, v6, C, v7, v8. C1[S _ v1 _ v2 _ v6] = C[K _ v7 _ v8] ∧ value(v1) ∧ value(v2) ∧ value(v6) ∧ value(v7) ∧ value(v8) ∧ context(C) → C1[v1 _ v6 _ (v2 _ v6)] = C[v7] ⊦ t _ C1[v3 _ v5 _ (v4 _ v5)] = C0[v]

Rule argument

[var-arg: C0]

Additional information

[[CONCRETESIMPRULES : ([CSIMPGEN : rawctxt generated by o, _, _;], [CSIMPSEQ : ⊦ context(C _ t) ↔ context(C)], [CSIMPSEQ : ⊦ t _ t0 = t1 _ t2 ↔ t = t1 ∧ t0 = t2], [CSIMPSEQ : ⊦ context(O)], [CSIMPSEQ : ⊦ value(K _ t) ↔ value(t)])]]