Nuprl Lemma : tfunequiv_wf
∀X,Y:Space. (tfunequiv(X;Y) ∈ EquivRel(topfun(X;Y);f,g.topfuneq(X;Y;f;g)))
Proof
Definitions occuring in Statement :
tfunequiv: tfunequiv(X;Y),
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],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
topfuneq-equiv-ext,
tfunequiv: tfunequiv(X;Y),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
topfuneq_wf,
topfun_wf,
equiv_rel_wf,
all_wf,
topspace_wf,
subtype_rel_self,
topfuneq-equiv-ext
Rules used in proof :
hypothesisEquality,
cumulativity,
lambdaEquality,
functionEquality,
isectElimination,
sqequalHypSubstitution,
introduction,
hypothesis,
extract_by_obid,
instantiate,
thin,
applyEquality,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}X,Y:Space. (tfunequiv(X;Y) \mmember{} EquivRel(topfun(X;Y);f,g.topfuneq(X;Y;f;g)))
Date html generated:
2018_07_29-AM-09_48_45
Last ObjectModification:
2018_06_21-AM-10_39_06
Theory : inner!product!spaces
Home
Index