Nuprl Lemma : l_disjoint-fpf-dom

∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f:a:A fp-> Top]. ∀[L:A List].
  uiff(l_disjoint(A;fst(f);L);∀[a:A]. ¬(a ∈ L) supposing ↑a ∈ dom(f))


Proof




Definitions occuring in Statement :  fpf-dom: x ∈ dom(f),  fpf: a:A fp-> B[a],  deq: EqDecider(T),  l_disjoint: l_disjoint(T;l1;l2),  l_member: (x ∈ l),  list: T List,  assert: ↑b,  uiff: uiff(P;Q),  uimplies: b supposing a,  uall: ∀[x:A]. B[x],  top: Top,  pi1: fst(t),  not: ¬A,  universe: Type
Lemmas :  l_member_wf,  assert_wf,  deq-member_wf,  all_wf,  not_wf,  uall_wf,  isect_wf,  list_wf,  top_wf,  deq_wf,  assert-deq-member
\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[f:a:A  fp->  Top].  \mforall{}[L:A  List].
    uiff(l\_disjoint(A;fst(f);L);\mforall{}[a:A].  \mneg{}(a  \mmember{}  L)  supposing  \muparrow{}a  \mmember{}  dom(f))



Date html generated: 2015_07_17-AM-11_16_18
Last ObjectModification: 2015_01_28-AM-07_38_18

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