[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 45 from proof termination-RED1 (previous step)

〈tn := none〉 tn = none, 〈RED1(t4; tn2)〉 tn2 = none, 〈RED1(t3; tn1)〉 tn1 = none, ∀ t0. #(t0) < #(t3 _ t4 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), value(t3 _ t4), value(t3), ¬ hasS(t2), ¬ hasS(t3), ¬ hasS(t4), ¬ (t3 = K ∧ value(t4) ∧ value(t2)), ¬ (ap(t3) ∧ t3 .1 = S), ¬ (ap(t3 _ t4) ∧ ap((t3 _ t4) .1) ∧ (t3 _ t4) .1 .1 = K ∧ value((t3 _ t4) .1 .2) ∧ value((t3 _ t4) .2)), ap(t3 _ t4) ∧ ap((t3 _ t4) .1) ∧ ap((t3 _ t4) .1 .1) ∧ (t3 _ t4) .1 .1 .1 = S, v = (t3 _ t4) .2, v0 = (t3 _ t4) .1 .2, v4 = (t3 _ t4) .1 .1 .2, ¬ (value(v4) ∧ value(v0) ∧ value(v)) ⊦ 〈RED1(t2; tn0)〉〈t1 := t3 _ t4 ; if tn0 ≠ none then tn0 := some(t1 _ tn0 .t)〉 (tn0 ≠ none → ¬ hasS(tn0) ∧ ¬ #(t1) + #(t2) < #(tn0))

Heuristic symbolic execution applied rule assign left

And obtained the following new goals

Proof step 44:
〈RED1(t4; tn2)〉 tn2 = none, 〈RED1(t3; tn1)〉 tn1 = none, ∀ t0. #(t0) < #(t3 _ t4 _ t2) → (¬ hasS(t0) → 〈RED1(t0; tn)〉 (tn ≠ none → ¬ hasS(tn) ∧ #(tn) < #(t0))), value(t3 _ t4), value(t3), ¬ hasS(t2), ¬ hasS(t3), ¬ hasS(t4), ¬ (t3 = K ∧ value(t4) ∧ value(t2)), ¬ (ap(t3) ∧ t3 .1 = S), ¬ (ap(t3 _ t4) ∧ ap((t3 _ t4) .1) ∧ (t3 _ t4) .1 .1 = K ∧ value((t3 _ t4) .1 .2) ∧ value((t3 _ t4) .2)), ap(t3 _ t4) ∧ ap((t3 _ t4) .1) ∧ ap((t3 _ t4) .1 .1) ∧ (t3 _ t4) .1 .1 .1 = S, v = (t3 _ t4) .2, v0 = (t3 _ t4) .1 .2, v4 = (t3 _ t4) .1 .1 .2, ¬ (value(v4) ∧ value(v0) ∧ value(v)), none = none ⊦ 〈RED1(t2; tn0)〉〈t1 := t3 _ t4 ; if tn0 ≠ none then tn0 := some(t1 _ tn0 .t)〉 (tn0 ≠ none → ¬ hasS(tn0) ∧ ¬ #(t1) + #(t2) < #(tn0))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]