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Proof step 172 from proof kappa-RED1 (previous step)

〈if tn4 ≠ none then tn4 := some(tn4 .t _ t .2) else if value(t .1) then { RED1(t .2; tn4): n -1 ; if tn4 ≠ none then tn4 := some(t .1 _ tn4 .t) }〉 tn4 = tn1, 〈RED1(t .1; tn3): n -1 〉 tn3 = tn4, 〈TOPRED(t; tn2): n -1 〉 tn2 = tn3, 〈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, tn3 = none ∧ ap(t) ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 57:
〈tn4 := some(tn4 .t _ t .2)〉 tn4 = tn1, 〈RED1(t .1; tn3): n -1 〉 tn3 = tn4, 〈TOPRED(t; tn2): n -1 〉 tn2 = tn3, 〈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, tn3 = none ∧ ap(t), tn4 ≠ none ⊦
Proof step 171:
〈if value(t .1) then { RED1(t .2; tn4): n -1 ; if tn4 ≠ none then tn4 := some(t .1 _ tn4 .t) }〉 tn4 = tn1, 〈RED1(t .1; tn3): n -1 〉 tn3 = tn4, 〈TOPRED(t; tn2): n -1 〉 tn2 = tn3, 〈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, tn3 = none ∧ ap(t), ¬ tn4 ≠ none ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

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