Nuprl Lemma : homeo-image_wf
∀[X,Y:Type]. ∀[dX:metric(X)]. ∀[dY:metric(Y)]. ∀[h:homeomorphic(X;dX;Y;dY)]. ∀[A:Type].
homeo-image(A;Y;dY;h) ∈ Type supposing A ⊆r X
Proof
Definitions occuring in Statement :
homeo-image: homeo-image(A;Y;dY;h),
homeomorphic: homeomorphic(X;dX;Y;dY),
metric: metric(X),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
homeo-image: homeo-image(A;Y;dY;h),
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
homeomorphic: homeomorphic(X;dX;Y;dY),
pi1: fst(t),
mfun: FUN(X ⟶ Y),
subtype_rel: A ⊆r B
Latex:
\mforall{}[X,Y:Type]. \mforall{}[dX:metric(X)]. \mforall{}[dY:metric(Y)]. \mforall{}[h:homeomorphic(X;dX;Y;dY)]. \mforall{}[A:Type].
homeo-image(A;Y;dY;h) \mmember{} Type supposing A \msubseteq{}r X
Date html generated:
2020_05_20-AM-11_50_49
Last ObjectModification:
2019_11_07-PM-01_50_40
Theory : reals
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