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Proof step 44 from proof kappa-TOPRED (previous step)

〈if value(v4) ∧ value(v0) ∧ value(v) then tn2 := some(v4 _ v _ (v0 _ v)) else tn2 := none〉 tn2 = tn1, 〈TOPRED(t; tn)〉 tn = tn0, tn0 ≠ tn1, tn2 = tn, n ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)), ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2 ⊦

Heuristic conditional left split applied rule if left

And obtained the following new goals

Proof step 27:
〈tn2 := some(v4 _ v _ (v0 _ v))〉 tn2 = tn1, 〈TOPRED(t; tn)〉 tn = tn0, tn0 ≠ tn1, tn2 = tn, n ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)), ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2, value(v4) ∧ value(v0) ∧ value(v) ⊦
Proof step 43:
〈tn2 := none〉 tn2 = tn1, 〈TOPRED(t; tn)〉 tn = tn0, tn0 ≠ tn1, tn2 = tn, n ≠ 0, ¬ (ap(t) ∧ ap(t .1) ∧ t .1 .1 = K ∧ value(t .1 .2) ∧ value(t .2)), ap(t) ∧ ap(t .1) ∧ ap(t .1 .1) ∧ t .1 .1 .1 = S, v = t .2, v0 = t .1 .2, v4 = t .1 .1 .2, ¬ (value(v4) ∧ value(v0) ∧ value(v)) ⊦

Rule argument

[fmapos-arg: pos: left 1]

Additional information

[[CONCRETESIMPRULES : ()]]