Nuprl Lemma : homeo-inv_wf
∀[X,Y:Type]. ∀[dX:metric(X)]. ∀[dY:metric(Y)]. ∀[h:homeomorphic(X;dX;Y;dY)]. (homeo-inv(h) ∈ homeomorphic(Y;dY;X;dX))
Proof
Definitions occuring in Statement :
homeo-inv: homeo-inv(h),
homeomorphic: homeomorphic(X;dX;Y;dY),
metric: metric(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
homeomorphic: homeomorphic(X;dX;Y;dY),
exists: ∃x:A. B[x],
sq_exists: ∃x:A [B[x]],
homeo-inv: homeo-inv(h),
and: P ∧ Q,
all: ∀x:A. B[x],
mfun: FUN(X ⟶ Y),
prop: ℙ
Latex:
\mforall{}[X,Y:Type]. \mforall{}[dX:metric(X)]. \mforall{}[dY:metric(Y)]. \mforall{}[h:homeomorphic(X;dX;Y;dY)].
(homeo-inv(h) \mmember{} homeomorphic(Y;dY;X;dX))
Date html generated:
2020_05_20-AM-11_41_50
Last ObjectModification:
2019_11_12-AM-09_53_56
Theory : reals
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