Nuprl Lemma : geo-congruent-between-exists
∀e:BasicGeometry. ∀a,b,c,a',c':Point.
(a # b ⇒ (∃b':Point. (B(a'b'c') ∧ ab ≅ a'b' ∧ bc ≅ b'c')) supposing (B(abc) and ac ≅ a'c'))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-between: B(abc),
geo-sep: a # b,
geo-point: Point,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
prop: ℙ,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
geo-between: B(abc),
false: False,
not: ¬A,
geo-congruent: ab ≅ cd,
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
all: ∀x:A. B[x],
basic-geometry: BasicGeometry,
exists: ∃x:A. B[x],
cand: A c∧ B,
basic-geometry-: BasicGeometry-,
euclidean-plane: EuclideanPlane,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,a',c':Point.
(a \# b {}\mRightarrow{} (\mexists{}b':Point. (B(a'b'c') \mwedge{} ab \mcong{} a'b' \mwedge{} bc \mcong{} b'c')) supposing (B(abc) and ac \mcong{} a'c'))
Date html generated:
2020_05_20-AM-09_52_16
Last ObjectModification:
2019_12_20-PM-08_45_20
Theory : euclidean!plane!geometry
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