Nuprl Lemma : geo-left-interiority
∀g:OrientedPlane. ∀a,b,c,p:Point. (p leftof ab ⇒ p leftof bc ⇒ p leftof ca ⇒ (¬a leftof cb))
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,
iff: P ⇐⇒ Q,
subtract: n - m,
cons: [a / b],
select: L[n],
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
lelt: i ≤ j < k,
int_seg: {i..j-},
top: Top,
l_all: (∀x∈L.P[x]),
geo-colinear-set: geo-colinear-set(e; L),
cand: A c∧ B,
geo-lsep: a # bc,
rev_implies: P ⇐ Q
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,c,p:Point. (p leftof ab {}\mRightarrow{} p leftof bc {}\mRightarrow{} p leftof ca {}\mRightarrow{} (\mneg{}a leftof cb))
Date html generated:
2020_05_20-AM-10_02_03
Last ObjectModification:
2019_12_26-PM-08_58_27
Theory : euclidean!plane!geometry
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