Nuprl Lemma : geo-left_functionality
∀e:EuclideanPlane. ∀a1,a2,b1,b2,c1,c2:Point. (a1 ≡ a2 ⇒ b1 ≡ b2 ⇒ c1 ≡ c2 ⇒ (a1 leftof b1c1 ⇐⇒ a2 leftof b2c2))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-eq: a ≡ b,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
basic-geo-axioms: BasicGeometryAxioms(g),
squash: ↓T,
geo-between: B(abc),
cand: A c∧ B,
not: ¬A,
geo-eq: a ≡ b,
geo-sep: a # b,
geo-gt-prim: ab>cd,
record-select: r.x,
geo-lsep: a # bc,
or: P ∨ Q
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a1,a2,b1,b2,c1,c2:Point.
(a1 \mequiv{} a2 {}\mRightarrow{} b1 \mequiv{} b2 {}\mRightarrow{} c1 \mequiv{} c2 {}\mRightarrow{} (a1 leftof b1c1 \mLeftarrow{}{}\mRightarrow{} a2 leftof b2c2))
Date html generated:
2020_05_20-AM-09_47_25
Last ObjectModification:
2020_01_27-PM-07_08_53
Theory : euclidean!plane!geometry
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