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Proof step 33 from proof RED1-lem (previous step)

〈TOPRED(t; tn)〉 tn = tn1, ∀ t0. #(t0) < #(t) → (true → 〈RED1(t0; tn)〉 (tn = none ⊃ irred(t0); t0 => tn .t)), tn1 = none ⊃ (∀ t0. ¬ t =>top t0) ; t =>top tn1 .t, ¬ (tn1 = none ∧ ap(t)), tn1 = none ⊃ ¬ irred(t) ; ¬ t => tn1 .t ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 32:
〈TOPRED(t; tn)〉 tn = tn1, ∀ t0. #(t0) < #(t) → (true → 〈RED1(t0; tn)〉 (tn = none ⊃ irred(t0); t0 => tn .t)), tn1 = none ⊃ (∀ t0. ¬ t =>top t0) ; t =>top tn1 .t, ¬ ap(t), tn1 = none ⊃ ¬ irred(t) ; ¬ t => tn1 .t ⊦

Rule argument

[CASEDARG : pos: left 4, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ t =>top t1 → (¬ t => t1 ↔ false)])]]