Nuprl Lemma : between-preserves-left-6
∀e:EuclideanPlane. ∀A,B,C,V:Point. (C leftof AB ⇒ B # V ⇒ B(VAB) ⇒ C leftof VB)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-between: B(abc),
geo-left: a leftof bc,
geo-sep: a # b,
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,
cand: A c∧ B,
or: P ∨ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
uimplies: b supposing a
Latex:
\mforall{}e:EuclideanPlane. \mforall{}A,B,C,V:Point. (C leftof AB {}\mRightarrow{} B \# V {}\mRightarrow{} B(VAB) {}\mRightarrow{} C leftof VB)
Date html generated:
2020_05_20-AM-09_59_11
Last ObjectModification:
2020_01_01-PM-05_22_12
Theory : euclidean!plane!geometry
Home
Index