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Proof step 269 from proof kappa-RED1 (previous step)

〈if ap(S _ t4 _ t3 _ t1) ∧ ap((S _ t4 _ t3 _ t1) .1) ∧ ap((S _ t4 _ t3 _ t1) .1 .1) ∧ (S _ t4 _ t3 _ t1) .1 .1 .1 = S then let v1 = (S _ t4 _ t3 _ t1) .1 .1 .2, v2 = (S _ t4 _ t3 _ t1) .1 .2, v3 = (S _ t4 _ t3 _ t1) .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn1 := some(v1 _ v3 _ (v2 _ v3)) else tn1 := none else tn1 := none〉 tn1 = tn0, ∀ 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, tn0 ≠ none, value(t4), value(t3), value(t1) ⊦

Heuristic symbolic execution applied rule if positive left

And obtained the following new goals

Proof step 268:
〈let v1 = (S _ t4 _ t3 _ t1) .1 .1 .2, v2 = (S _ t4 _ t3 _ t1) .1 .2, v3 = (S _ t4 _ t3 _ t1) .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn1 := some(v1 _ v3 _ (v2 _ v3)) else tn1 := none〉 tn1 = tn0, ∀ 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, tn0 ≠ none, value(t4), value(t3), value(t1) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ap(t _ t0)], [CSIMPSEQ : ⊦ (t _ t0) .1 = t])]]