Nuprl Lemma : left-transitivity
∀g:OrientedPlane. ∀a,b,x,y,z:Point.
(x leftof ab ⇒ y leftof ab ⇒ z leftof ab ⇒ y leftof ax ⇒ z leftof ay ⇒ (¬z leftof xa))
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
exists: ∃x:A. B[x],
euclidean-plane: EuclideanPlane,
oriented-plane: OrientedPlane,
member: t ∈ T,
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
stable: Stable{P},
geo-eq: a ≡ b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
cand: A c∧ B
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,x,y,z:Point.
(x leftof ab {}\mRightarrow{} y leftof ab {}\mRightarrow{} z leftof ab {}\mRightarrow{} y leftof ax {}\mRightarrow{} z leftof ay {}\mRightarrow{} (\mneg{}z leftof xa))
Date html generated:
2020_05_20-AM-10_02_17
Last ObjectModification:
2019_12_26-PM-08_58_07
Theory : euclidean!plane!geometry
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