Nuprl Lemma : geo-lt-angle-or
∀e:EuclideanPlane. ∀b,y:Point. ∀a,c:{p:Point| p # b} . ∀x,z:{q:Point| q # y} . (¬¬(xyz < abc ∨ abc < xyz ∨ abc ≅a xyz))
Proof
Definitions occuring in Statement :
geo-lt-angle: abc < xyz,
geo-cong-angle: abc ≅a xyz,
euclidean-plane: EuclideanPlane,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
or: P ∨ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
stable: Stable{P},
iff: P ⇐⇒ Q,
and: P ∧ Q,
geo-lsep: a # bc,
exists: ∃x:A. B[x],
cand: A c∧ B,
geo-out: out(p ab),
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),
satisfiable_int_formula: satisfiable_int_formula(fmla),
select: L[n],
cons: [a / b],
subtract: n - m,
geo-lt-angle: abc < xyz,
geo-colinear: Colinear(a;b;c),
oriented-plane: OrientedPlane,
geo-eq: a ≡ b,
rev_implies: P ⇐ Q,
geo-strict-between: a-b-c,
basic-geometry-: BasicGeometry-,
geo-cong-angle: abc ≅a xyz
Latex:
\mforall{}e:EuclideanPlane. \mforall{}b,y:Point. \mforall{}a,c:\{p:Point| p \# b\} . \mforall{}x,z:\{q:Point| q \# y\} .
(\mneg{}\mneg{}(xyz < abc \mvee{} abc < xyz \mvee{} abc \mcong{}\msuba{} xyz))
Date html generated:
2020_05_20-AM-10_41_37
Last ObjectModification:
2020_01_13-PM-05_30_17
Theory : euclidean!plane!geometry
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