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Proof step 27 from proof RED1-lem (previous step)

〈TOPRED(t1 _ t2; tn)〉 tn = none, ∀ t0. #(t0) < #(t1 _ t2) → (true → 〈RED1(t0; tn)〉 (tn = none ⊃ irred(t0); t0 => tn .t)), ∀ t0. ¬ t1 _ t2 =>top t0 ⊦ 〈RED1(t1; tn1)〉〈if tn1 ≠ none then tn1 := some(tn1 .t _ t2) else if value(t1) then { RED1(t2; tn1) ; if tn1 ≠ none then tn1 := some(t1 _ tn1 .t) }〉 (tn1 = none ⊃ irred(t1 _ t2); t1 _ t2 => tn1 .t)

User applied rule apply induction

And obtained the following new goals

Proof step 26:
〈RED1(t1; tn)〉 (tn = none ⊃ irred(t1); t1 => tn .t), 〈TOPRED(t1 _ t2; tn)〉 tn = none, ∀ t0. #(t0) < #(t1 _ t2) → (true → 〈RED1(t0; tn)〉 (tn = none ⊃ irred(t0); t0 => tn .t)), ∀ t0. ¬ t1 _ t2 =>top t0 ⊦ 〈RED1(t1; tn1)〉〈if tn1 ≠ none then tn1 := some(tn1 .t _ t2) else if value(t1) then { RED1(t2; tn1) ; if tn1 ≠ none then tn1 := some(t1 _ tn1 .t) }〉 (tn1 = none ⊃ irred(t1 _ t2); t1 _ t2 => tn1 .t)

Rule argument

[substlist-arg: [t0] → [t1]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ #(t _ t0) = (#(t) + #(t0)) +1], [CSIMPSEQ : ⊦ m +1 = m + 1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (t1)]]