Nuprl Lemma : ss-sep_functionality
∀ss:SeparationSpace. ∀x,y,x',y':Point. (x ≡ x' ⇒ y ≡ y' ⇒ {x # y ⇐⇒ x' # y'})
Proof
Definitions occuring in Statement :
ss-eq: x ≡ y,
ss-sep: x # y,
ss-point: Point,
separation-space: SeparationSpace,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
false: False,
not: ¬A,
ss-eq: x ≡ y,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
guard: {T},
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
ss-eq_inversion,
ss-sep-or,
separation-space_wf,
ss-point_wf,
ss-eq_wf,
ss-sep_wf
Rules used in proof :
independent_pairFormation,
voidElimination,
unionElimination,
independent_functionElimination,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
cut
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y,x',y':Point. (x \mequiv{} x' {}\mRightarrow{} y \mequiv{} y' {}\mRightarrow{} \{x \# y \mLeftarrow{}{}\mRightarrow{} x' \# y'\})
Date html generated:
2016_11_08-AM-09_11_14
Last ObjectModification:
2016_11_02-PM-03_05_24
Theory : inner!product!spaces
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