Nuprl Lemma : ss-eq_weakening
∀ss:SeparationSpace. ∀x,y:Point. ((x = y ∈ Point) ⇒ x ≡ y)
Proof
Definitions occuring in Statement :
ss-eq: x ≡ y,
ss-point: Point,
separation-space: SeparationSpace,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
false: False,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
not: ¬A,
ss-eq: x ≡ y,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
ss-sep-irrefl,
iff_weakening_equal,
true_wf,
squash_wf,
separation-space_wf,
ss-point_wf,
equal_wf,
ss-sep_wf
Rules used in proof :
voidElimination,
independent_functionElimination,
productElimination,
independent_isectElimination,
universeEquality,
baseClosed,
imageMemberEquality,
sqequalRule,
natural_numberEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
lambdaEquality,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y:Point. ((x = y) {}\mRightarrow{} x \mequiv{} y)
Date html generated:
2016_11_08-AM-09_11_04
Last ObjectModification:
2016_10_31-AM-11_09_31
Theory : inner!product!spaces
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