Nuprl Lemma : geo-eq_transitivity
∀[e:BasicGeometry-]. ∀[a,b,c:Point]. (a ≡ c) supposing (b ≡ c and a ≡ b)
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-eq: a ≡ b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-eq: a ≡ b,
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
guard: {T},
all: ∀x:A. B[x],
basic-geometry-: BasicGeometry-,
euclidean-plane: EuclideanPlane,
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[e:BasicGeometry-]. \mforall{}[a,b,c:Point]. (a \mequiv{} c) supposing (b \mequiv{} c and a \mequiv{} b)
Date html generated:
2020_05_20-AM-09_48_45
Last ObjectModification:
2020_01_13-PM-03_13_21
Theory : euclidean!plane!geometry
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