Nuprl Lemma : geo-lt-angle-trans
∀g:EuclideanPlane. ∀a,b,c,d,e,f,x,y,z:Point. (abc < def ⇒ def < xyz ⇒ a # bc ⇒ d # ef ⇒ x # yz ⇒ abc < xyz)
Proof
Definitions occuring in Statement :
geo-lt-angle: abc < xyz,
euclidean-plane: EuclideanPlane,
geo-lsep: a # bc,
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,
exists: ∃x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
cand: A c∧ B,
basic-geometry: BasicGeometry,
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
select: L[n],
cons: [a / b],
subtract: n - m,
geo-out: out(p ab),
geo-cong-angle: abc ≅a xyz,
geo-cong-tri: Cong3(abc,a'b'c'),
uiff: uiff(P;Q),
geo-strict-between: a-b-c,
geo-sep: a # b,
basic-geometry-: BasicGeometry-
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c,d,e,f,x,y,z:Point.
(abc < def {}\mRightarrow{} def < xyz {}\mRightarrow{} a \# bc {}\mRightarrow{} d \# ef {}\mRightarrow{} x \# yz {}\mRightarrow{} abc < xyz)
Date html generated:
2020_05_20-AM-10_32_10
Last ObjectModification:
2020_01_14-PM-00_40_18
Theory : euclidean!plane!geometry
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