Nuprl Lemma : colinear-implies-midpoint
∀e:BasicGeometry. ∀M,A,B:Point. (A # B ⇒ Colinear(A;M;B) ⇒ MA ≅ MB ⇒ A=M=B)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-midpoint: a=m=b,
geo-colinear: Colinear(a;b;c),
geo-congruent: ab ≅ cd,
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,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
geo-midpoint: a=m=b,
and: P ∧ Q,
uiff: uiff(P;Q),
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
geo-strict-between: a-b-c,
not: ¬A,
false: False,
squash: ↓T,
true: True,
geo-zero-length: 0,
geo-eq: a ≡ b
Latex:
\mforall{}e:BasicGeometry. \mforall{}M,A,B:Point. (A \# B {}\mRightarrow{} Colinear(A;M;B) {}\mRightarrow{} MA \mcong{} MB {}\mRightarrow{} A=M=B)
Date html generated:
2020_05_20-AM-09_57_30
Last ObjectModification:
2020_01_13-PM-03_32_18
Theory : euclidean!plane!geometry
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