Nuprl Lemma : geo-incident-iff-not-plsep
∀[e:EuclideanPlane]. ∀[x:Point]. ∀[m:Line]. (x I m ⇐⇒ ¬x # m)
Proof
Definitions occuring in Statement :
geo-plsep: p # l,
geo-incident: p I L,
geo-line: Line,
euclidean-plane: EuclideanPlane,
geo-point: Point,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
or: P ∨ Q,
geo-plsep: p # l,
geo-incident: p I L,
all: ∀x:A. B[x]
Latex:
\mforall{}[e:EuclideanPlane]. \mforall{}[x:Point]. \mforall{}[m:Line]. (x I m \mLeftarrow{}{}\mRightarrow{} \mneg{}x \# m)
Date html generated:
2020_05_20-AM-10_46_27
Last ObjectModification:
2019_12_03-AM-09_47_22
Theory : euclidean!plane!geometry
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