Nuprl Lemma : Euclid-Prop2-lemma
∀e:EuclideanPlane. ∀a:Point. ∀b:{b:Point| a # b} . ∀v:Point. (∃x:Point [ax ≅ bv])
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
sq_exists: ∃x:A [B[x]],
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
geo-congruent: ab ≅ cd,
not: ¬A,
false: False,
squash: ↓T,
exists: ∃x:A. B[x],
cand: A c∧ B,
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,
satisfiable_int_formula: satisfiable_int_formula(fmla),
select: L[n],
cons: [a / b],
subtract: n - m,
basic-geometry-: BasicGeometry-,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
oriented-plane: OrientedPlane,
append: as @ bs,
so_lambda: so_lambda3,
top: Top,
so_apply: x[s1;s2;s3],
geo-strict-between: a-b-c,
geo-eq: a ≡ b
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a:Point. \mforall{}b:\{b:Point| a \# b\} . \mforall{}v:Point. (\mexists{}x:Point [ax \mcong{} bv])
Date html generated:
2020_05_20-AM-09_51_08
Last ObjectModification:
2020_01_27-PM-10_03_20
Theory : euclidean!plane!geometry
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