Nuprl - Pf closed_rel_mng

(10steps) PrintForm Definitions Lemmas mb automata 3 Sections GenAutomata Doc

1. s: Top
2. e: Top
3. a1: Top
4. a2: Top
5. tr: Top
6. l: Term List
7. u: Term
8. v: Term List
9. X:Top. reduce(t,vs. term_free_vars(t) @ vs;nil;v) = nil (list_accum(x,t.x([[t]] 1of(e) s a1 tr);X;v) ~ list_accum(x,t.x([[t]] 1of(e) s a2 tr);X;v))
10. X: Top
11. (term_free_vars(u) @ reduce(t,vs. term_free_vars(t) @ vs;nil;v)) = nil
12. list_accum(x,t.x ([[t]] 1of(e) s a1 tr);X ([[u]] 1of(e) s a1 tr);v) ~ list_accum(x,t....;X (...);v)

[[u]] 1of(e) s a2 tr ~ [[u]] 1of(e) s a1 tr

By: Thin -1 THEN BackThru Thm* t:Term, e,s,a1,a2,tr:Top. closed_term(t) ([[t]] e s a1 tr ~ [[t]] e s a2 tr) THEN RWO "append_is_nil" -1

Generated subgoal:

1 11. term_free_vars(u) = nil
12. reduce(t,vs. term_free_vars(t) @ vs;nil;v) = nil
closed_term(u)

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(10steps) PrintForm Definitions Lemmas mb automata 3 Sections GenAutomata Doc