Nuprl Lemma : subtype-fpf-cap

[X:Type]. ∀[eq:EqDecider(X)]. ∀[f,g:x:X fp-> Type].  {∀[x:X]. (f(x)?Top ⊆g(x)?Top)} supposing g ⊆ f


Proof




Definitions occuring in Statement :  fpf-sub: f ⊆ g fpf-cap: f(x)?z fpf: a:A fp-> B[a] deq: EqDecider(T) uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] top: Top guard: {T} universe: Type
Lemmas :  fpf-dom_wf subtype-fpf2 top_wf subtype_top bool_wf fpf-ap_wf equal-wf-T-base assert_wf bnot_wf not_wf eqtt_to_assert uiff_transitivity eqff_to_assert assert_of_bnot
\mforall{}[X:Type].  \mforall{}[eq:EqDecider(X)].  \mforall{}[f,g:x:X  fp->  Type].
    \{\mforall{}[x:X].  (f(x)?Top  \msubseteq{}r  g(x)?Top)\}  supposing  g  \msubseteq{}  f



Date html generated: 2015_07_17-AM-09_17_49
Last ObjectModification: 2015_01_28-AM-07_51_21

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