Nuprl Lemma : p5geo
∀e:BasicGeometry. ∀a,b,c:Point. ((ab ≅ ac ∧ Triangle(a;b;c)) ⇒ (∃j,k:Point. (jbc ≅a kcb ∧ B(abj) ∧ B(ack))))
Proof
Definitions occuring in Statement :
geo-cong-angle: abc ≅a xyz,
geo-tri: Triangle(a;b;c),
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-between: B(abc),
geo-point: Point,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
geo-tri: Triangle(a;b;c),
basic-geometry: BasicGeometry,
exists: ∃x:A. B[x],
geo-cong-angle: abc ≅a xyz,
cand: A c∧ B,
uiff: uiff(P;Q),
true: True,
squash: ↓T
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point.
((ab \mcong{} ac \mwedge{} Triangle(a;b;c)) {}\mRightarrow{} (\mexists{}j,k:Point. (jbc \mcong{}\msuba{} kcb \mwedge{} B(abj) \mwedge{} B(ack))))
Date html generated:
2020_05_20-AM-09_59_01
Last ObjectModification:
2020_01_27-PM-10_00_32
Theory : euclidean!plane!geometry
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