Nuprl Lemma : homeo-image-homeomorphic-subtype
∀[X,Y:Type]. ∀[dX:metric(X)]. ∀[dY:metric(Y)]. ∀[h:homeomorphic(X;dX;Y;dY)]. ∀[A:Type].
h ∈ homeomorphic(A;dX;homeo-image(A;Y;dY;h);dY) supposing metric-subspace(X;dX;A)
Proof
Definitions occuring in Statement :
homeo-image: homeo-image(A;Y;dY;h),
metric-subspace: metric-subspace(X;d;A),
homeomorphic: homeomorphic(X;dX;Y;dY),
metric: metric(X),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
metric-subspace: metric-subspace(X;d;A),
and: P ∧ Q,
uiff: uiff(P;Q),
homeomorphic: homeomorphic(X;dX;Y;dY),
exists: ∃x:A. B[x],
sq_exists: ∃x:A [B[x]],
homeo-image: homeo-image(A;Y;dY;h),
mfun: FUN(X ⟶ Y),
subtype_rel: A ⊆r B,
pi1: fst(t),
prop: ℙ,
is-mfun: f:FUN(X;Y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_apply: x[s]
Latex:
\mforall{}[X,Y:Type]. \mforall{}[dX:metric(X)]. \mforall{}[dY:metric(Y)]. \mforall{}[h:homeomorphic(X;dX;Y;dY)]. \mforall{}[A:Type].
h \mmember{} homeomorphic(A;dX;homeo-image(A;Y;dY;h);dY) supposing metric-subspace(X;dX;A)
Date html generated:
2020_05_20-AM-11_51_51
Last ObjectModification:
2019_11_07-PM-02_37_47
Theory : reals
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