Nuprl - Pf closed rel mng 2 1 2 2 2 1 1 1 1 2 1 2

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At: closed rel mng 2 1 2 2 2 1 1 1 1 2 1 2

1. r: rel()
2. rho: Decl{i}
3. ds: Collection{i}(dec())
4. daa: Collection{i}(dec())
5. da1: Collection{i}(SimpleType)
6. da2: Collection{i}(SimpleType)
7. de: sig()
8. s: {[[ds]] rho}
9. e: {sig_mng{i:l} (de; rho)}
10. a1: Top
11. a2: Top
12. tr: trace_env([[daa]] rho)
13. trace_consistent_rel(rho;daa;tr.proj;r)
14. tc(r;ds;da1;de)
15. tc(r;ds; < > ;de) & a1 [[ < > ]] rho & a2 [[ < > ]] rho
16. aa: Term List
17. u: Term
18. v: Term List
19. xx:Top. reduce(t,vs. term_free_vars(t) @ vs;nil;v) = nil (list_accum(x,t.x([[t]] 1of(e) s a2 tr);xx;v) ~ list_accum(x,t.x([[t]] 1of(e) s a1 tr);xx;v))
20. xx: Top
21. (term_free_vars(u) @ reduce(t,vs. term_free_vars(t) @ vs;nil;v)) = nil
22. u1: TermType{i'}
23. w: u:{v1:Term| u1(v1) }term_iterate(f.nil;f.nil;f.nil;v.[v];P.nil;x,y. x @ y;u) = nil (iterate(statevar x- > s.x statevar x'- > s.x funsymbol f- > 1of(e).f freevar x- > a2 trace(P)- > tr.P x(y)- > x(y) over u) ~ iterate(statevar x- > s.x statevar x'- > s.x funsymbol f- > 1of(e).f freevar x- > a1 trace(P)- > tr.P x(y)- > x(y) over u))
24. y1: {v1:Term| u1(v1) }
25. y2: {v1:Term| u1(v1) }

(term_iterate(f.nil;f.nil;f.nil;v.[v];P.nil;x,y. x @ y;y1) @ term_iterate(f.nil;f.nil;f.nil;v.[v];P.nil;x,y. x @ y;y2)) = nil ((iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a2 trace(t)- > tr.t x(y)- > x(y) over y1) (iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a2 trace(t)- > tr.t x(y)- > x(y) over y2))) ~ (iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a1 trace(t)- > tr.t x(y)- > x(y) over y1) (iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a1 trace(t)- > tr.t x(y)- > x(y) over y2))))

By: Analyze 0

Generated subgoal:

1 26. (term_iterate(f.nil; f.nil; f.nil; v.[v]; P.nil; x,y. x @ y; y1) @ term_iterate(f.nil; f.nil; f.nil; v.[v]; P.nil; x,y. x @ y; y2)) = nil
(iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a2 trace(t)- > tr.t x(y)- > x(y) over y1) (iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a2 trace(t)- > tr.t x(y)- > x(y) over y2))) ~ (iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a1 trace(t)- > tr.t x(y)- > x(y) over y1) (iterate(statevar x- > s.x statevar x'- > s.x funsymbol x- > 1of(e).x freevar x- > a1 trace(t)- > tr.t x(y)- > x(y) over y2)))

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(24steps) PrintForm Definitions Lemmas mb automata 4 Sections GenAutomata Doc