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Proof step 312 from proof kappa-RED1 (previous step)

〈if n = 0 then abort else { TOPRED(t; tn2): n -1 ; if tn2 = none ∧ ap(t) then { RED1(t .1; tn2): n -1 ; if tn2 ≠ none then tn2 := some(tn2 .t _ t .2) else if value(t .1) then { RED1(t .2; tn2): n -1 ; if tn2 ≠ none then tn2 := some(t .1 _ tn2 .t) } } }〉 tn2 = tn1, 〈RED1(t; tn)〉 tn = tn0, ∀ n0, t, tn1, tn0. n0 < n → (〈RED1(t; tn): n0 〉 tn = tn1 ∧ 〈RED1(t; tn)〉 tn = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, tn2 = tn ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 2:
〈abort〉 tn2 = tn1, 〈RED1(t; tn)〉 tn = tn0, ∀ n0, t, tn1, tn0. n0 < n → (〈RED1(t; tn): n0 〉 tn = tn1 ∧ 〈RED1(t; tn)〉 tn = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, tn2 = tn, n = 0 ⊦
Proof step 311:
〈TOPRED(t; tn2): n -1 〉〈if tn2 = none ∧ ap(t) then { RED1(t .1; tn2): n -1 ; if tn2 ≠ none then tn2 := some(tn2 .t _ t .2) else if value(t .1) then { RED1(t .2; tn2): n -1 ; if tn2 ≠ none then tn2 := some(t .1 _ tn2 .t) } }〉 tn2 = tn1, 〈RED1(t; tn)〉 tn = tn0, ∀ n0, t, tn1, tn0. n0 < n → (〈RED1(t; tn): n0 〉 tn = tn1 ∧ 〈RED1(t; tn)〉 tn = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ tn1, tn2 = tn, n ≠ 0 ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

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