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Proof step 297 from proof kappa-RED1 (previous step)

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

Heuristic split applied rule split left

And obtained the following new goals

Proof step 296:
〈if tn2 = none ∧ ap(t) then { RED1(t .1; tn2) ; if tn2 ≠ none then tn2 := some(tn2 .t _ t .2) else if value(t .1) then { RED1(t .2; tn2) ; if tn2 ≠ none then tn2 := some(t .1 _ tn2 .t) } }〉 tn2 = tn0, 〈TOPRED(t; 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 ≠ none, m ≠ 0, ¬ ap(t) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]