Nuprl Lemma : topeq-equiv
∀X:Space. EquivRel(|X|;a,b.topeq(X;a;b))
Proof
Definitions occuring in Statement :
topeq: topeq(X;a;b),
toptype: |X|,
topspace: Space,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x]
Definitions unfolded in proof :
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
pi2: snd(t),
pi1: fst(t),
all: ∀x:A. B[x],
topspace: Space,
toptype: |X|,
topeq: topeq(X;a;b)
Lemmas referenced :
equiv_rel_wf
Rules used in proof :
applyEquality,
lambdaEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
hypothesisEquality,
cumulativity,
functionEquality,
universeEquality,
productEquality,
hypothesis,
thin,
productElimination,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}X:Space. EquivRel(|X|;a,b.topeq(X;a;b))
Date html generated:
2018_07_29-AM-09_47_52
Last ObjectModification:
2018_06_21-AM-10_28_53
Theory : inner!product!spaces
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