Nuprl - Pf closed_rel_mng2 1 1 2 1 2 1

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

1. s: Top
2. s': Top
3. e: Top
4. a1: Top
5. a2: Top
6. tr: Top
7. l: Term List
8. u: Term
9. v: Term List
10. X:Top. reduce(t,vs. term_free_vars(t) @ vs;nil;v) = nil (list_accum(x,t.x([[t]] 1of(e) s s' a1 tr);X;v) ~ list_accum(x,t.x([[t]] 1of(e) s s' a2 tr);X;v))
11. X: Top
12. (term_free_vars(u) @ reduce(t,vs. term_free_vars(t) @ vs;nil;v)) = nil
13. list_accum(x,t.x ([[t]] 1of(e) s s' a1 tr);X ([[u]] 1of(e) s s' a1 tr);v) ~ list_accum(x,t.x (...);...;v)

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

By: Thin -1 THEN BackThru Thm* t:Term, e,s,s',a1,a2,tr:Top. closed_term(t) ([[t]] e s s' a1 tr ~ [[t]] e s s' a2 tr) THEN RWO "append_is_nil" -1

Generated subgoal:

1 12. term_free_vars(u) = nil
13. 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