Nuprl Lemma : geo-congruent-preserves-between
∀e:BasicGeometry. ∀[a,b,c,a',b',c':Point]. (B(a'b'c')) supposing (bc ≅ b'c' and ac ≅ a'c' and ab ≅ a'b' and B(abc))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-between: B(abc),
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-between: B(abc),
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
or: P ∨ Q,
stable: Stable{P},
geo-eq: a ≡ b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
uiff: uiff(P;Q)
Latex:
\mforall{}e:BasicGeometry
\mforall{}[a,b,c,a',b',c':Point]. (B(a'b'c')) supposing (bc \mcong{} b'c' and ac \mcong{} a'c' and ab \mcong{} a'b' and B(abc))
Date html generated:
2020_05_20-AM-09_52_24
Last ObjectModification:
2019_12_20-PM-08_45_10
Theory : euclidean!plane!geometry
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