Nuprl Lemma : left-between
∀g:OrientedPlane. ∀a,b,x,y,z:Point. (x leftof ab ⇒ y leftof ab ⇒ B(xzy) ⇒ z leftof ab)
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-between: B(abc),
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
oriented-plane: OrientedPlane,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
guard: {T},
uimplies: b supposing a,
basic-geo-axioms: BasicGeometryAxioms(g),
and: P ∧ Q,
geo-lsep: a # bc,
or: P ∨ Q,
false: False,
not: ¬A
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,x,y,z:Point. (x leftof ab {}\mRightarrow{} y leftof ab {}\mRightarrow{} B(xzy) {}\mRightarrow{} z leftof ab)
Date html generated:
2020_05_20-AM-09_50_11
Last ObjectModification:
2020_01_27-PM-07_08_39
Theory : euclidean!plane!geometry
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