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Proof step 303 from proof kappa-RED1 (previous step)

〈if m = 0 then abort else if ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2) then tn3 := some(t .1 .2) else 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 tn3 := some(v1 _ v3 _ (v2 _ v3)) else tn3 := none else tn3 := none〉 tn3 = tn1, 〈RED1(t; tn2)〉 tn2 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, ¬ (tn1 = none ∧ ap(t)), tn3 = tn2 ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 175:
〈abort〉 tn3 = tn1, 〈RED1(t; tn2)〉 tn2 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, ¬ (tn1 = none ∧ ap(t)), tn3 = tn2, m = 0 ⊦
Proof step 302:
〈if ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2) then tn3 := some(t .1 .2) else 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 tn3 := some(v1 _ v3 _ (v2 _ v3)) else tn3 := none else tn3 := none〉 tn3 = tn1, 〈RED1(t; tn2)〉 tn2 = tn0, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, ¬ (tn1 = none ∧ ap(t)), tn3 = tn2, m ≠ 0 ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

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