Nuprl Lemma : trivial-homeo-image
∀[X,Y:Type]. ∀[dX:metric(X)]. ∀[dY:metric(Y)]. ∀[h:homeomorphic(X;dX;Y;dY)]. homeo-image(X;Y;dY;h) ≡ Y
Proof
Definitions occuring in Statement :
homeo-image: homeo-image(A;Y;dY;h),
homeomorphic: homeomorphic(X;dX;Y;dY),
metric: metric(X),
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
homeo-image: homeo-image(A;Y;dY;h),
homeomorphic: homeomorphic(X;dX;Y;dY),
exists: ∃x:A. B[x],
sq_exists: ∃x:A [B[x]],
pi1: fst(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
mfun: FUN(X ⟶ Y),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[X,Y:Type]. \mforall{}[dX:metric(X)]. \mforall{}[dY:metric(Y)]. \mforall{}[h:homeomorphic(X;dX;Y;dY)].
homeo-image(X;Y;dY;h) \mequiv{} Y
Date html generated:
2020_05_20-AM-11_51_30
Last ObjectModification:
2019_11_18-PM-11_22_16
Theory : reals
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