Nuprl Lemma : ss-sep-symmetry
∀ss:SeparationSpace. ∀x,y:Point(ss). (x # y ⇒ y # x)
Proof
Definitions occuring in Statement :
ss-sep: x # y,
ss-point: Point(ss),
separation-space: SeparationSpace,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
ss-sep_wf,
ss-point_wf,
separation-space_wf,
ss-sep-or,
ss-sep-irrefl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
universeIsType,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
voidElimination
Latex:
\mforall{}ss:SeparationSpace. \mforall{}x,y:Point(ss). (x \# y {}\mRightarrow{} y \# x)
Date html generated:
2019_10_31-AM-07_26_20
Last ObjectModification:
2019_09_19-PM-04_06_13
Theory : constructive!algebra
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