[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 10 from proof ks-RED (previous step)

∀ n0. n0 < n → (true → 〈RED(ks(n0); t)〉 ((even(n0) → t = K) ∧ (odd(n0) → t = K _ K))), n = 0 ∨ n = 1, ap(ks(n)) ∧ ap(ks(n) .1) ∧ ks(n) .1 .1 = K ∧ value(ks(n) .1 .2) ∧ value(ks(n) .2), tn0 = some(ks(n) .1 .2) ⊦ 〈if tn0 = none ∧ ap(ks(n)) then { RED1(ks(n) .1; tn0) ; if tn0 ≠ none then tn0 := some(tn0 .t _ ks(n) .2) else if value(ks(n) .1) then { RED1(ks(n) .2; tn0) ; if tn0 ≠ none then tn0 := some(ks(n) .1 _ tn0 .t) } }〉〈if tn0 ≠ none then RED(tn0 .t; t0) else t0 := ks(n)〉 ((even(n) → t0 = K) ∧ (odd(n) → t0 = K _ K))

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 9:
∀ n0. n0 < n → (true → 〈RED(ks(n0); t)〉 ((even(n0) → t = K) ∧ (odd(n0) → t = K _ K))), n = 0 ∨ n = 1, ap(ks(n)) ∧ ap(ks(n) .1) ∧ ks(n) .1 .1 = K ∧ value(ks(n) .1 .2) ∧ value(ks(n) .2), tn0 = some(ks(n) .1 .2) ⊦ 〈skip〉〈if tn0 ≠ none then RED(tn0 .t; t0) else t0 := ks(n)〉 ((even(n) → t0 = K) ∧ (odd(n) → t0 = K _ K))

Rule argument

[fmapos-arg: pos: right 1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ some(t) ≠ none])]]