Nuprl Lemma : topeq_wf
∀[X:Space]. ∀[a,b:|X|]. (topeq(X;a;b) ∈ ℙ)
Proof
Definitions occuring in Statement :
topeq: topeq(X;a;b),
toptype: |X|,
topspace: Space,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_apply: x[s],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
so_lambda: λ2x.t[x],
prop: ℙ,
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x],
topspace: Space,
toptype: |X|,
topeq: topeq(X;a;b)
Lemmas referenced :
top_wf,
subtype_rel_product,
equiv_rel_wf,
pi2_wf,
pi1_wf_top
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaFormation,
independent_isectElimination,
because_Cache,
productEquality,
lambdaEquality,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
hypothesisEquality,
independent_pairEquality,
productElimination,
universeEquality,
cumulativity,
functionEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
applyEquality,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[X:Space]. \mforall{}[a,b:|X|]. (topeq(X;a;b) \mmember{} \mBbbP{})
Date html generated:
2018_07_29-AM-09_47_47
Last ObjectModification:
2018_06_21-AM-10_18_17
Theory : inner!product!spaces
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