Nuprl Lemma : geo-between-outer-trans
∀e:BasicGeometry-. ∀[a,b,c,d:Point]. (B(acd)) supposing (B(bcd) and B(abc) and b # c)
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-between: B(abc),
geo-sep: a # b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-between: B(abc),
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
basic-geometry-: BasicGeometry-,
euclidean-plane: EuclideanPlane,
or: P ∨ Q,
stable: Stable{P},
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x]
Latex:
\mforall{}e:BasicGeometry-. \mforall{}[a,b,c,d:Point]. (B(acd)) supposing (B(bcd) and B(abc) and b \# c)
Date html generated:
2020_05_20-AM-09_51_41
Last ObjectModification:
2020_01_13-PM-03_25_03
Theory : euclidean!plane!geometry
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