Nuprl Lemma : geo-lt-angle-degenerate-case2
∀e:EuclideanPlane. ∀a,b,x,y,z:Point. (a # b ⇒ x # yz ⇒ aba < xyz)
Proof
Definitions occuring in Statement :
geo-lt-angle: abc < xyz,
euclidean-plane: EuclideanPlane,
geo-lsep: a # 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,
geo-lt-angle: abc < xyz,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
not: ¬A,
basic-geometry: BasicGeometry,
iff: P ⇐⇒ Q,
geo-colinear: Colinear(a;b;c),
cand: A c∧ B,
exists: ∃x:A. B[x],
false: False,
geo-out: out(p ab),
geo-cong-angle: abc ≅a xyz,
geo-sep: a # b,
geo-between: B(abc)
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,x,y,z:Point. (a \# b {}\mRightarrow{} x \# yz {}\mRightarrow{} aba < xyz)
Date html generated:
2020_05_20-AM-10_07_27
Last ObjectModification:
2019_12_03-AM-09_51_45
Theory : euclidean!plane!geometry
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