Nuprl Lemma : basic-axioms-imply_between1
∀e:EuclideanPlaneStructure. (BasicGeometryAxioms(e) ⇒ (∀a1,a2,b,c:Point. (a1 ≡ a2 ⇒ B(a1bc) ⇒ B(a2bc))))
Proof
Definitions occuring in Statement :
euclidean-plane-structure: EuclideanPlaneStructure,
basic-geo-axioms: BasicGeometryAxioms(g),
geo-eq: a ≡ b,
geo-between: B(abc),
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
and: P ∧ Q,
subtype_rel: A ⊆r B,
basic-geo-axioms: BasicGeometryAxioms(g),
uall: ∀[x:A]. B[x],
prop: ℙ,
geo-between: B(abc),
cand: A c∧ B,
not: ¬A,
geo-lsep: a # bc,
or: P ∨ Q,
false: False,
guard: {T},
geo-sep: a # b,
geo-eq: a ≡ b,
geo-ge: ab ≥ cd,
geo-congruent: ab ≅ cd,
geo-length-sep: ab # cd)
Latex:
\mforall{}e:EuclideanPlaneStructure
(BasicGeometryAxioms(e) {}\mRightarrow{} (\mforall{}a1,a2,b,c:Point. (a1 \mequiv{} a2 {}\mRightarrow{} B(a1bc) {}\mRightarrow{} B(a2bc))))
Date html generated:
2020_05_20-AM-09_43_13
Last ObjectModification:
2020_01_27-PM-10_46_12
Theory : euclidean!plane!geometry
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