Nuprl Lemma : homeomorphic_wf
∀[X,Y:Type]. ∀[dX:metric(X)]. ∀[dY:metric(Y)]. (homeomorphic(X;dX;Y;dY) ∈ ℙ)
Proof
Definitions occuring in Statement :
homeomorphic: homeomorphic(X;dX;Y;dY),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
homeomorphic: homeomorphic(X;dX;Y;dY),
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
mfun: FUN(X ⟶ Y)
Lemmas referenced :
mfun_wf,
equal-wf-T-base,
compose_wf,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
functionEquality,
setElimination,
rename,
baseClosed,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X,Y:Type]. \mforall{}[dX:metric(X)]. \mforall{}[dY:metric(Y)]. (homeomorphic(X;dX;Y;dY) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-06_23_14
Last ObjectModification:
2019_10_02-AM-09_58_54
Theory : reals
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