Nuprl Lemma : geo-congruent-full-symmetry
∀e:EuclideanPlane
∀[a,b,c,d:Point]. {ba ≅ cd ∧ ab ≅ dc ∧ ba ≅ dc ∧ cd ≅ ab ∧ dc ≅ ab ∧ cd ≅ ba ∧ dc ≅ ba} supposing ab ≅ cd
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-congruent: ab ≅ cd,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
and: P ∧ Q,
geo-congruent: ab ≅ cd,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
cand: A c∧ B,
geo-length-sep: ab # cd),
or: P ∨ Q,
euclidean-plane: EuclideanPlane,
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}e:EuclideanPlane
\mforall{}[a,b,c,d:Point].
\{ba \mcong{} cd \mwedge{} ab \mcong{} dc \mwedge{} ba \mcong{} dc \mwedge{} cd \mcong{} ab \mwedge{} dc \mcong{} ab \mwedge{} cd \mcong{} ba \mwedge{} dc \mcong{} ba\} supposing ab \mcong{} cd
Date html generated:
2020_05_20-AM-09_45_33
Last ObjectModification:
2020_01_27-PM-04_55_11
Theory : euclidean!plane!geometry
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