Nuprl Lemma : topfuneq-equiv
∀X,Y:Space. EquivRel(topfun(X;Y);f,g.topfuneq(X;Y;f;g))
Proof
Definitions occuring in Statement :
topfuneq: topfuneq(X;Y;f;g),
topfun: topfun(X;Y),
topspace: Space,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
topfun: topfun(X;Y),
topfuneq: topfuneq(X;Y;f;g),
trans: Trans(T;x,y.E[x; y]),
prop: ℙ,
implies: P ⇒ Q,
sym: Sym(T;x,y.E[x; y]),
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Lemmas referenced :
topeq_transitivity,
topeq_inversion,
toptype_wf,
topeq_weakening,
topspace_wf,
topfuneq_wf,
topfun_wf
Rules used in proof :
independent_functionElimination,
rename,
setElimination,
applyEquality,
dependent_functionElimination,
because_Cache,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}X,Y:Space. EquivRel(topfun(X;Y);f,g.topfuneq(X;Y;f;g))
Date html generated:
2018_07_29-AM-09_48_29
Last ObjectModification:
2018_06_21-AM-10_27_55
Theory : inner!product!spaces
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