Nuprl Lemma : geo-sep-irrefl'
∀e:EuclideanPlane. ∀[a:Point]. False supposing a ≠ a
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],
false: False
Definitions unfolded in proof :
implies: P ⇒ Q,
not: ¬A,
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
geo-sep-irrefl2,
geo-point_wf,
geo-primitives_wf,
euclidean-plane-structure_wf,
euclidean-plane_wf,
subtype_rel_transitivity,
euclidean-plane-subtype,
euclidean-plane-structure-subtype,
geo-sep_wf
Rules used in proof :
dependent_functionElimination,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
voidElimination,
isect_memberEquality,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
because_Cache,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:EuclideanPlane. \mforall{}[a:Point]. False supposing a \mneq{} a
Date html generated:
2017_10_02-PM-04_40_19
Last ObjectModification:
2017_08_08-PM-01_49_21
Theory : euclidean!plane!geometry
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