[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 647 from proof SII-loops (previous step)

〈if m0 = 0 then abort else if ap(t1) ∧ ap(t1 .1) ∧ t1 .1 .1 = K ∧ value(t1 .1 .2) ∧ value(t1 .2) then tn0 := some(t1 .1 .2) else if ap(t1) ∧ ap(t1 .1) ∧ ap(t1 .1 .1) ∧ t1 .1 .1 .1 = S then let v1 = t1 .1 .1 .2, v2 = t1 .1 .2, v3 = t1 .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn0 := some(v1 _ v3 _ (v2 _ v3)) else tn0 := none else tn0 := none〉〈tn1 := tn0 ; if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m0 + 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < (m0 + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false), tn0 = tn1 ∧ t1 = S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 646:
〈if m0 = 0 then abort else let v1 = S _ K _ K, v2 = S _ K _ K, v3 = S _ (S _ K _ K) _ (S _ K _ K) in if value(v1) ∧ value(v2) ∧ value(v3) then tn0 := some(v1 _ v3 _ (v2 _ v3)) else tn0 := none〉〈tn1 := tn0 ; if tn1 = none then { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ (S _ K _ K) _ (S _ K _ K))) else { RED1(S _ (S _ K _ K) _ (S _ K _ K); tn1): m0 ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) } }〉〈if tn1 ≠ none then RED(tn1 .t; t3): m0 + 1 else t3 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K))〉 t3 = t, ∀ kappa0, t. kappa0 < (m0 + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t3): kappa0 〉 t3 = t → false) ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ t _ t0 ≠ K], [CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t])]]