Nuprl Lemma : lsep-iff
∀g:OrientedPlane. ∀a,b,c:Point. (a # bc ⇐⇒ (∀y:Point. (y # b ⇒ Colinear(y;b;c) ⇒ a # by)) ∧ c # b)
Proof
Definitions occuring in Statement :
oriented-plane: OrientedPlane,
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
cand: A c∧ B,
oriented-plane: OrientedPlane,
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),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
select: L[n],
cons: [a / b],
subtract: n - m,
rev_implies: P ⇐ Q
Latex:
\mforall{}g:OrientedPlane. \mforall{}a,b,c:Point.
(a \# bc \mLeftarrow{}{}\mRightarrow{} (\mforall{}y:Point. (y \# b {}\mRightarrow{} Colinear(y;b;c) {}\mRightarrow{} a \# by)) \mwedge{} c \# b)
Date html generated:
2020_05_20-AM-09_50_17
Last ObjectModification:
2019_12_20-PM-08_01_57
Theory : euclidean!plane!geometry
Home
Index