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Proof step 286 from proof kappa-RED1 (previous step)

〈if value(v4) ∧ value(v0) ∧ value(v) then tn3 := some(v4 _ v _ (v0 _ v)) 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, ¬ (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, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2 ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 284:
〈tn3 := some(v4 _ v _ (v0 _ v))〉 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, ¬ (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, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2, value(v4) ∧ value(v0) ∧ value(v) ⊦
Proof step 285:
〈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, ¬ (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, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2, ¬ (value(v4) ∧ value(v0) ∧ value(v)) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

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