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Proof step 25 from proof RED1-lem (previous step)

〈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)

User applied rule if right

And obtained the following new goals

Proof step 3:
〈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, tn0 ≠ none ⊦ 〈tn0 := some(tn0 .t _ t2)〉 (tn0 = none ⊃ irred(t1 _ t2); t1 _ t2 => tn0 .t)
Proof step 24:
〈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, ¬ tn0 ≠ none ⊦ 〈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

[fmapos-arg: pos: right 1]

Additional information

[[CONCRETESIMPRULES : ()]]