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Proof step 133 from proof kappa-RED1 (previous step)

〈if tn5 = none ∧ ap(t0 _ t1) then { RED1((t0 _ t1) .1; tn5) ; if tn5 ≠ none then tn5 := some(tn5 .t _ (t0 _ t1) .2) else if value((t0 _ t1) .1) then { RED1((t0 _ t1) .2; tn5) ; if tn5 ≠ none then tn5 := some((t0 _ t1) .1 _ tn5 .t) } }〉 tn5 = tn0, 〈TOPRED(t0 _ t1; tn)〉 tn = tn5, 〈RED1(t1; tn4): m 〉 tn4 = none, 〈RED1(t0; tn3): m 〉 tn3 = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ none, value(t0) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 107:
〈TOPRED(t; tn)〉 tn = tn0, 〈TOPRED(t; tn): n 〉 tn = tn1 ⊦ tn0 = tn1
Proof step 111:
〈if tn5 = none ∧ ap(t0 _ t1) then { RED1((t0 _ t1) .1; tn5) ; if tn5 ≠ none then tn5 := some(tn5 .t _ (t0 _ t1) .2) else if value((t0 _ t1) .1) then { RED1((t0 _ t1) .2; tn5) ; if tn5 ≠ none then tn5 := some((t0 _ t1) .1 _ tn5 .t) } }〉 tn5 = tn0, 〈TOPRED(t0 _ t1; tn)〉 tn = tn5, 〈RED1(t1; tn4): m 〉 tn4 = none, 〈RED1(t0; tn3): m 〉 tn3 = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ none, value(t0) ⊦ 〈TOPRED(t0 _ t1; tn): m 〉 tn = none
Proof step 132:
〈if tn5 = none ∧ ap(t0 _ t1) then { RED1((t0 _ t1) .1; tn5) ; if tn5 ≠ none then tn5 := some(tn5 .t _ (t0 _ t1) .2) else if value((t0 _ t1) .1) then { RED1((t0 _ t1) .2; tn5) ; if tn5 ≠ none then tn5 := some((t0 _ t1) .1 _ tn5 .t) } }〉 tn5 = tn0, 〈TOPRED(t0 _ t1; tn)〉 tn = tn5, 〈RED1(t1; tn4): m 〉 tn4 = none, 〈RED1(t0; tn3): m 〉 tn3 = none, 〈TOPRED(t0 _ t1; tn2): m 〉 tn2 = none, ∀ n0, t, tn1, tn0. n0 < m + 1 → (〈RED1(t; tn2): n0 〉 tn2 = tn1 ∧ 〈RED1(t; tn2)〉 tn2 = tn0 ∧ tn0 ≠ tn1 → false), tn0 ≠ none, value(t0), tn5 = none ⊦

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: kappa-TOPRED antecedent: 〈TOPRED(t; tn)〉 tn = tn0, 〈TOPRED(t; tn): n 〉 tn = tn1 succedent: tn0 = tn1 substlist: [t, tn0, n, tn1] → [t0 _ t1, tn5, m, none] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (t0 _ t1, tn5, m, none)]]