Nuprl Lemma : left-right-colinear-cases
∀e:EuclideanPlane. ∀u,v,b,c:Point.
(∀a:Point. (a # b ⇒ Colinear(a;b;u) ⇒ Colinear(a;b;v) ⇒ (B(abu) ∨ B(abv)))) supposing (v leftof cb and u leftof bc)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-colinear: Colinear(a;b;c),
geo-between: B(abc),
geo-left: a leftof bc,
geo-sep: a # b,
geo-point: Point,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
member: t ∈ T,
sq_stable: SqStable(P),
squash: ↓T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
geo-lsep: a # bc,
or: P ∨ Q,
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
select: L[n],
cons: [a / b],
subtract: n - m,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
cand: A c∧ B,
stable: Stable{P}
Latex:
\mforall{}e:EuclideanPlane. \mforall{}u,v,b,c:Point.
(\mforall{}a:Point. (a \# b {}\mRightarrow{} Colinear(a;b;u) {}\mRightarrow{} Colinear(a;b;v) {}\mRightarrow{} (B(abu) \mvee{} B(abv)))) supposing
(v leftof cb and
u leftof bc)
Date html generated:
2020_05_20-AM-09_49_53
Last ObjectModification:
2020_01_13-PM-03_21_16
Theory : euclidean!plane!geometry
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