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Proof step 87 from proof ks-RED (previous step)

∀ n0. n0 < n → (true → 〈RED(ks(n0); t)〉 ((even(n0) → t = K) ∧ (odd(n0) → t = K _ K))), n = 0 ∨ n = 1 ⊦ 〈TOPRED(ks(n); tn)〉〈if tn = none ∧ ap(ks(n)) then { RED1(ks(n) .1; tn) ; if tn ≠ none then tn := some(tn .t _ ks(n) .2) else if value(ks(n) .1) then { RED1(ks(n) .2; tn) ; if tn ≠ none then tn := some(ks(n) .1 _ tn .t) } }〉〈if tn ≠ none then RED(tn .t; t0) else t0 := ks(n)〉 ((even(n) → t0 = K) ∧ (odd(n) → t0 = K _ K))

User applied rule call right

And obtained the following new goals

Proof step 3:
⊦
Proof step 86:
∀ n0. n0 < n → (true → 〈RED(ks(n0); t)〉 ((even(n0) → t = K) ∧ (odd(n0) → t = K _ K))), n = 0 ∨ n = 1 ⊦ 〈if ap(ks(n)) ∧ ap(ks(n) .1) ∧ ks(n) .1 .1 = K ∧ value(ks(n) .1 .2) ∧ value(ks(n) .2) then tn0 := some(ks(n) .1 .2) else if ap(ks(n)) ∧ ap(ks(n) .1) ∧ ap(ks(n) .1 .1) ∧ ks(n) .1 .1 .1 = S then let v1 = ks(n) .1 .1 .2, v2 = ks(n) .1 .2, v3 = ks(n) .2 in if value(v1) ∧ value(v2) ∧ value(v3) then tn0 := some(v1 _ v3 _ (v2 _ v3)) else tn0 := none else tn0 := none〉〈tn := tn0 ; if tn = none ∧ ap(ks(n)) then { RED1(ks(n) .1; tn) ; if tn ≠ none then tn := some(tn .t _ ks(n) .2) else if value(ks(n) .1) then { RED1(ks(n) .2; tn) ; if tn ≠ none then tn := some(ks(n) .1 _ tn .t) } }〉〈if tn ≠ none then RED(tn .t; t0) else t0 := ks(n)〉 ((even(n) → t0 = K) ∧ (odd(n) → t0 = K _ K))

Rule argument

[fmapos-arg: pos: right 1]

Additional information

[[CONCRETESIMPRULES : ()]]