Nuprl Lemma : geo-sep-irrefl2
∀e:EuclideanPlane. ∀[a,b:Point]. ¬(a = b ∈ Point) supposing a ≠ b
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-sep: a ≠ b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
euclidean-plane_wf,
geo-sep_wf,
geo-point_wf,
equal_wf,
geo-sep-irrefl
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
lambdaEquality,
sqequalRule,
applyEquality,
because_Cache,
voidElimination,
independent_functionElimination,
hypothesis,
independent_isectElimination,
isectElimination,
hypothesisEquality,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
thin,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a,b:Point]. \mneg{}(a = b) supposing a \mneq{} b
Date html generated:
2017_10_02-PM-04_40_16
Last ObjectModification:
2017_08_08-PM-01_49_00
Theory : euclidean!plane!geometry
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