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Proof step 58 from proof kappa-TOPRED (previous step)

〈if ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S then let v1 = t .1 .1 .2, v2 = t .1 .2, v3 = t .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn2 := some(v1 _ v3 _ (v2 _ v3)) else tn2 := none else tn2 := none〉 tn2 = tn1, 〈TOPRED(t; tn)〉 tn = tn0, tn0 ≠ tn1, tn2 = tn, n ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)) ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 45:
〈let v1 = t .1 .1 .2, v2 = t .1 .2, v3 = t .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn2 := some(v1 _ v3 _ (v2 _ v3)) else tn2 := none〉 tn2 = tn1, 〈TOPRED(t; tn)〉 tn = tn0, tn0 ≠ tn1, tn2 = tn, n ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)), ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S ⊦
Proof step 57:
〈tn2 := none〉 tn2 = tn1, 〈TOPRED(t; tn)〉 tn = tn0, tn0 ≠ tn1, tn2 = tn, n ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)), ¬ (ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

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