Nuprl Lemma : geo-sum-eq-x
∀e:BasicGeometry. ∀a,b,c,d:Point. ((X = |ab| + |cd| ∈ Length) ⇒ (a ≡ b ∧ c ≡ d))
Proof
Definitions occuring in Statement :
geo-add-length: p + q,
geo-length: |s|,
geo-length-type: Length,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-X: X,
geo-eq: a ≡ b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
prop: ℙ
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Point. ((X = |ab| + |cd|) {}\mRightarrow{} (a \mequiv{} b \mwedge{} c \mequiv{} d))
Date html generated:
2020_05_20-AM-09_57_51
Last ObjectModification:
2020_01_13-PM-03_41_16
Theory : euclidean!plane!geometry
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