Nuprl Lemma : ss-sep_test
∀ss:SeparationSpace. ∀x,y,z,w,a:Point. (y ≡ x ⇒ y ≡ z ⇒ w ≡ z ⇒ w # a ⇒ x # a)
Proof
Definitions occuring in Statement :
ss-eq: x ≡ y,
ss-sep: x # y,
ss-point: Point,
separation-space: SeparationSpace,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
ss-eq_weakening,
ss-sep_functionality,
ss-eq_transitivity,
ss-eq_inversion,
separation-space_wf,
ss-point_wf,
ss-eq_wf,
ss-sep_wf
Rules used in proof :
because_Cache,
independent_functionElimination,
dependent_functionElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y,z,w,a:Point. (y \mequiv{} x {}\mRightarrow{} y \mequiv{} z {}\mRightarrow{} w \mequiv{} z {}\mRightarrow{} w \# a {}\mRightarrow{} x \# a)
Date html generated:
2016_11_08-AM-09_11_18
Last ObjectModification:
2016_10_31-PM-05_35_39
Theory : inner!product!spaces
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