Nuprl Lemma : topeq_weakening
∀X:Space. ∀a,b:|X|. ((a = b ∈ |X|) ⇒ topeq(X;a;b))
Proof
Definitions occuring in Statement :
topeq: topeq(X;a;b),
toptype: |X|,
topspace: Space,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
refl: Refl(T;x,y.E[x; y]),
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
and: P ∧ Q,
equiv_rel: EquivRel(T;x,y.E[x; y]),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
topeq_wf,
and_wf,
topspace_wf,
toptype_wf,
equal_wf,
topeq-equiv
Rules used in proof :
rename,
setElimination,
applyLambdaEquality,
independent_pairFormation,
dependent_set_memberEquality,
sqequalRule,
equalitySymmetry,
hyp_replacement,
isectElimination,
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}X:Space. \mforall{}a,b:|X|. ((a = b) {}\mRightarrow{} topeq(X;a;b))
Date html generated:
2018_07_29-AM-09_47_56
Last ObjectModification:
2018_06_21-AM-10_28_13
Theory : inner!product!spaces
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