Nuprl Lemma : ss-eq_transitivity
∀ss:SeparationSpace. ∀x,y,z:Point. (x ≡ y ⇒ y ≡ z ⇒ x ≡ z)
Proof
Definitions occuring in Statement :
ss-eq: x ≡ y,
ss-point: Point,
separation-space: SeparationSpace,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
false: False,
or: P ∨ Q,
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-symmetry,
separation-space_wf,
ss-point_wf,
ss-eq_wf,
ss-sep_wf,
ss-sep-or
Rules used in proof :
voidElimination,
unionElimination,
isectElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y,z:Point. (x \mequiv{} y {}\mRightarrow{} y \mequiv{} z {}\mRightarrow{} x \mequiv{} z)
Date html generated:
2016_11_08-AM-09_11_08
Last ObjectModification:
2016_10_31-AM-11_13_44
Theory : inner!product!spaces
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