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Proof step 45 from proof ks-RED1 (previous step)

〈RED1(ks(n0); tn)〉 tn = tn0, tn0 = none → n0 ≤ 1, tn0 ≠ none → ¬ n0 ≤ 1 ∧ tn0 = some(ks(n0 - 2)), ¬ (ap(ks(n0) _ K) ∧ ap((ks(n0) _ K) .1) ∧ (ks(n0) _ K) .1 .1 = K ∧ value((ks(n0) _ K) .1 .2) ∧ value((ks(n0) _ K) .2)), ap(ks(n0) _ K) ∧ ap((ks(n0) _ K) .1) ∧ ap((ks(n0) _ K) .1 .1) ∧ (ks(n0) _ K) .1 .1 .1 = S, v = (ks(n0) _ K) .2, v0 = (ks(n0) _ K) .1 .2, v4 = (ks(n0) _ K) .1 .1 .2, ¬ (value(v4) ∧ value(v0) ∧ value(v)) ⊦ 〈tn0 := none〉〈if tn0 = none ∧ ap(ks(n0) _ K) then { RED1((ks(n0) _ K) .1; tn0) ; if tn0 ≠ none then tn0 := some(tn0 .t _ (ks(n0) _ K) .2) else if value((ks(n0) _ K) .1) then { RED1((ks(n0) _ K) .2; tn0) ; if tn0 ≠ none then tn0 := some((ks(n0) _ K) .1 _ tn0 .t) } }〉 ((tn0 = none → n0 = 0) ∧ (tn0 ≠ none → n0 ≠ 0 ∧ tn0 = some(ks(n0 + 1 - 2))))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 44:
〈RED1(ks(n0); tn)〉 tn = tn0, tn0 = none → n0 ≤ 1, tn0 ≠ none → ¬ n0 ≤ 1 ∧ tn0 = some(ks(n0 - 2)), ¬ (ap(ks(n0) _ K) ∧ ap((ks(n0) _ K) .1) ∧ (ks(n0) _ K) .1 .1 = K ∧ value((ks(n0) _ K) .1 .2) ∧ value((ks(n0) _ K) .2)), ap(ks(n0) _ K) ∧ ap((ks(n0) _ K) .1) ∧ ap((ks(n0) _ K) .1 .1) ∧ (ks(n0) _ K) .1 .1 .1 = S, v = (ks(n0) _ K) .2, v0 = (ks(n0) _ K) .1 .2, v4 = (ks(n0) _ K) .1 .1 .2, ¬ (value(v4) ∧ value(v0) ∧ value(v)), tn = none ⊦ 〈if tn = none ∧ ap(ks(n0) _ K) then { RED1((ks(n0) _ K) .1; tn) ; if tn ≠ none then tn := some(tn .t _ (ks(n0) _ K) .2) else if value((ks(n0) _ K) .1) then { RED1((ks(n0) _ K) .2; tn) ; if tn ≠ none then tn := some((ks(n0) _ K) .1 _ tn .t) } }〉 ((tn = none → n0 = 0) ∧ (tn ≠ none → n0 ≠ 0 ∧ tn = some(ks(n0 + 1 - 2))))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]