[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 40 from proof reduction-is-topred-in-ctxt (previous step)

C = v4 _ C0, ∀ 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]), t0 _ t1 = C[K _ v _ v0] ∧ t' = C[v] ∧ value(v) ∧ value(v0) ∧ context(C) ∨ t0 _ t1 = C[S _ v1 _ v2 _ v3] ∧ t' = C[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C) ⊦ ∃ 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 39:
∀ 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]), t0 _ t1 = v4 _ C0[K _ v _ v0] ∧ t' = v4 _ C0[v] ∧ value(v) ∧ value(v0) ∧ context(C0) ∧ value(v4) ∨ t0 _ t1 = v4 _ C0[S _ v1 _ v2 _ v3] ∧ t' = v4 _ C0[v1 _ v3 _ (v2 _ v3)] ∧ value(v1) ∧ value(v2) ∧ value(v3) ∧ context(C0) ∧ value(v4) ⊦ ∃ C, t2, t3. context(C) ∧ t0 _ t1 = C[t2] ∧ t2 =>top t3 ∧ t' = C[t3]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ context(t _ C) ↔ ¬ ¬ (context(C) ∧ value(t))], [CSIMPSEQ : ⊦ (t1 _ C)[t] = t1 _ C[t]])]]