Nuprl Lemma : geo-cong-angle-symm
∀e:BasicGeometry. ∀a,b,c:Point. ((a # b ∧ c # b) ⇒ abc ≅a cba)
Proof
Definitions occuring in Statement :
geo-cong-angle: abc ≅a xyz,
basic-geometry: BasicGeometry,
geo-sep: a # b,
geo-point: Point,
all: ∀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,
geo-cong-angle: abc ≅a xyz,
cand: A c∧ B,
member: t ∈ T,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
uiff: uiff(P;Q),
squash: ↓T,
true: True,
exists: ∃x:A. B[x]
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. ((a \# b \mwedge{} c \# b) {}\mRightarrow{} abc \mcong{}\msuba{} cba)
Date html generated:
2020_05_20-AM-09_54_15
Last ObjectModification:
2020_01_27-PM-10_01_20
Theory : euclidean!plane!geometry
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