Nuprl Lemma : ss-eq_functionality
∀ss:SeparationSpace. ∀x1,x2,y1,y2:Point. (uiff(x1 ≡ y1;x2 ≡ y2)) supposing (y1 ≡ y2 and x1 ≡ x2)
Proof
Definitions occuring in Statement :
ss-eq: x ≡ y,
ss-point: Point,
separation-space: SeparationSpace,
uiff: uiff(P;Q),
uimplies: b supposing a,
all: ∀x:A. B[x]
Definitions unfolded in proof :
prop: ℙ,
uall: ∀[x:A]. B[x],
false: False,
not: ¬A,
ss-eq: x ≡ y,
implies: P ⇒ Q,
guard: {T},
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
separation-space_wf,
ss-point_wf,
ss-eq_wf,
ss-sep_wf,
ss-eq_transitivity,
ss-eq_inversion
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_pairEquality,
productElimination,
voidElimination,
isectElimination,
because_Cache,
lambdaEquality,
sqequalRule,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x1,x2,y1,y2:Point. (uiff(x1 \mequiv{} y1;x2 \mequiv{} y2)) supposing (y1 \mequiv{} y2 and x1 \mequiv{} x2)
Date html generated:
2016_11_08-AM-09_11_10
Last ObjectModification:
2016_10_31-PM-02_10_45
Theory : inner!product!spaces
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