[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 210 from proof kappa-RED1 (previous step)

〈if tn2 = none ∧ ap(K _ t3 _ t1) then { RED1((K _ t3 _ t1) .1; tn2) ; if tn2 ≠ none then tn2 := some(tn2 .t _ (K _ t3 _ t1) .2) else if value((K _ t3 _ t1) .1) then { RED1((K _ t3 _ t1) .2; tn2) ; if tn2 ≠ none then tn2 := some((K _ t3 _ t1) .1 _ tn2 .t) } }〉 tn2 = tn0, 〈TOPRED(K _ t3 _ t1; tn)〉 tn = tn2, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(t3), m ≠ 0, value(t3), value(t1) ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 203:
〈RED1((K _ t3 _ t1) .1; tn2)〉〈if tn2 ≠ none then tn2 := some(tn2 .t _ (K _ t3 _ t1) .2) else if value((K _ t3 _ t1) .1) then { RED1((K _ t3 _ t1) .2; tn2) ; if tn2 ≠ none then tn2 := some((K _ t3 _ t1) .1 _ tn2 .t) }〉 tn2 = tn0, 〈TOPRED(K _ t3 _ t1; tn)〉 tn = tn2, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(t3), m ≠ 0, value(t3), value(t1), tn2 = none ∧ ap(K _ t3 _ t1) ⊦
Proof step 209:
〈skip〉 tn2 = tn0, 〈TOPRED(K _ t3 _ t1; tn)〉 tn = tn2, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(t3), m ≠ 0, value(t3), value(t1), ¬ (tn2 = none ∧ ap(K _ t3 _ t1)) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]