Nuprl - Pf rel subst mng 2 iff 1 2 1 1 1

(65steps) (too big for print form) Definitions Lemmas mb automata 4 Sections GenAutomata Doc

1. r: rel()
2. as: (LabelTerm) List
3. ds: Collection(dec())
4. daa: Collection(dec())
5. da: Collection(SimpleType)
6. de: sig()
7. rho: Decl
8. e: {[[de]] rho}
9. s: {[[ds]] rho}
10. s': {[[ds]] rho}
11. k: Label
12. a: [[da]] rho
13. tr: trace_env([[daa]] rho)
14. trace_consistent_rel(rho;daa;tr.proj;r)
15. tc(r;ds;da;de)
16. subst_mentions_trace(as)
17. x:Label. (x rel_primed_vars(r)) (t:SimpleType. mk_dec(x, t) ds t term_types(ds;da;de;apply_alist(as;x;x)) & s'.x = [[apply_alist(as;x;x)]] 1of(e) s a tr [[t]] rho)
18. tc(rel_subst2(as;r);ds;da;de)
19. trace_consistent_rel(rho;daa;tr.proj;rel_subst2(as;r))
20. ||rel_subst2(as;r).args|| = ||r.args||
21. i:
22. i < ||rel_subst2(as;r).args||
23. x,y:Term. x = y (x ~ y)

rel_subst2(as;r).args[i] = term_subst2(as;r.args[i])

By: Unfold `rel_subst2` 0 THEN Reduce 0 THEN RWO "map_select" 0 THEN Reduce 0

Generated subgoals:

None

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(65steps) (too big for print form) Definitions Lemmas mb automata 4 Sections GenAutomata Doc