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Proof step 264 from proof kappa-RED1 (previous step)

〈RED1((S _ t4 _ t3 _ t1) .1; tn2)〉〈if tn2 ≠ none then tn2 := some(tn2 .t _ (S _ t4 _ t3 _ t1) .2) else if value((S _ t4 _ t3 _ t1) .1) then { RED1((S _ t4 _ t3 _ t1) .2; tn2) ; if tn2 ≠ none then tn2 := some((S _ t4 _ t3 _ t1) .1 _ tn2 .t) }〉 tn2 = tn0, 〈TOPRED(S _ t4 _ t3 _ t1; tn)〉 tn = tn2, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(t4 _ t1 _ (t3 _ t1)), m ≠ 0, value(t4), value(t3), value(t1), tn2 = none ∧ ap(S _ t4 _ t3 _ t1) ⊦

Heuristic split applied rule split left

And obtained the following new goals

Proof step 263:
〈if tn4 ≠ none then tn4 := some(tn4 .t _ (S _ t4 _ t3 _ t1) .2) else if value((S _ t4 _ t3 _ t1) .1) then { RED1((S _ t4 _ t3 _ t1) .2; tn4) ; if tn4 ≠ none then tn4 := some((S _ t4 _ t3 _ t1) .1 _ tn4 .t) }〉 tn4 = tn0, 〈RED1((S _ t4 _ t3 _ t1) .1; tn2)〉 tn2 = tn4, 〈TOPRED(S _ t4 _ t3 _ t1; tn)〉 tn = tn2, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn3): n0 〉 tn3 = tn1 ∧ 〈RED1(t; tn3)〉 tn3 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ some(t4 _ t1 _ (t3 _ t1)), m ≠ 0, value(t4), value(t3), value(t1), tn2 = none ∧ ap(S _ t4 _ t3 _ t1) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]