[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 525 from proof SII-loops (previous step)

〈TOPRED(t1; tn1): m0 -1 〉〈if tn1 = none ∧ ap(t1) then { RED1(t1 .1; tn1): m0 -1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ t1 .2) else if value(t1 .1) then { RED1(t1 .2; tn1): m0 -1 ; if tn1 ≠ none then tn1 := some(t1 .1 _ tn1 .t) } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn): m0 ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ tn .t) }〉〈tn1 := tn ; m := m0 + 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) }〉〈if tn1 ≠ none then RED(tn1 .t; t2): 1 + m else t2 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t2 = t, ∀ kappa0, t. kappa0 < (((((m0 + 1) + 1) + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t2): kappa0 〉 t2 = t → false), m0 ≠ 0, tn1 = tn ∧ t1 = S _ (S _ K _ K) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 524:
〈TOPRED(S _ (S _ K _ K); tn1): m0 - 1 〉〈if tn1 = none then { RED1(S; tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn1): m0 - 1 ; if tn1 ≠ none then tn1 := some(S _ tn1 .t) } }〉〈tn := tn1 ; if tn ≠ none then tn := some(tn .t _ (S _ K _ K)) else { RED1(S _ K _ K; tn): m0 ; if tn ≠ none then tn := some(S _ (S _ K _ K) _ tn .t) }〉〈tn1 := tn ; m := m0 + 1 ; if tn1 ≠ none then tn1 := some(tn1 .t _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))) else { RED1(S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)); tn1): m ; if tn1 ≠ none then tn1 := some(S _ (S _ K _ K) _ (S _ K _ K) _ tn1 .t) }〉〈if tn1 ≠ none then RED(tn1 .t; t2): 1 + m else t2 := S _ (S _ K _ K) _ (S _ K _ K) _ (S _ K _ K _ (S _ (S _ K _ K) _ (S _ K _ K)))〉 t2 = t, ∀ kappa0, t. kappa0 < (((((m0 + 1) + 1) + 1) + 1) + 1) + 1 → (〈RED(S _ (S _ K _ K) _ (S _ K _ K) _ (S _ (S _ K _ K) _ (S _ K _ K)); t2): kappa0 〉 t2 = t → false), m0 ≠ 0 ⊦

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ value(S)], [CSIMPSEQ : ⊦ (t _ t0) .2 = t0], [CSIMPSEQ : ⊦ (t _ t0) .1 = t], [CSIMPSEQ : ⊦ n -1 = n - 1])]]