Nuprl Lemma : topfuneq_wf
∀[X,Y:Space]. ∀[f,g:topfun(X;Y)]. (topfuneq(X;Y;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
topfuneq: topfuneq(X;Y;f;g),
topfun: topfun(X;Y),
topspace: Space,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
topfun: topfun(X;Y),
so_lambda: λ2x.t[x],
topfuneq: topfuneq(X;Y;f;g),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
topspace_wf,
topfun_wf,
topeq_wf,
toptype_wf,
all_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
rename,
setElimination,
applyEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X,Y:Space]. \mforall{}[f,g:topfun(X;Y)]. (topfuneq(X;Y;f;g) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-09_48_24
Last ObjectModification:
2018_06_21-AM-10_12_57
Theory : inner!product!spaces
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