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Proof step 26 from proof RED1-lem (previous step)

〈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)

Heuristic contract and execute applied rule execute call

And obtained the following new goals

Proof step 25:
〈RED1(t1; tn)〉 tn = tn0, 〈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, tn0 = none ⊃ irred(t1) ; t1 => tn0 .t ⊦ 〈if tn0 ≠ none then tn0 := some(tn0 .t _ t2) else if value(t1) then { RED1(t2; tn0) ; if tn0 ≠ none then tn0 := some(t1 _ tn0 .t) }〉 (tn0 = none ⊃ irred(t1 _ t2); t1 _ t2 => tn0 .t)

Rule argument

[fmaposlist-arg: (pos: left 1, pos: right 1)]

Additional information

[[CONCRETESIMPRULES : ()]]