Nuprl Lemma : geo-5segSAS
∀e:BasicGeometry. ∀a,b,c,f,g,A,B,C,F,G:Point.
(af ≅ AF ∧ fb ≅ FB ∧ bc ≅ BC ∧ ag ≅ AG ∧ gc ≅ GC) ⇒ fg ≅ FG supposing B(afb) ∧ B(agc) ∧ B(AFB) ∧ B(AGC)
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-congruent: ab ≅ cd,
geo-between: B(abc),
geo-point: Point,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
geo-congruent: ab ≅ cd,
not: ¬A,
false: False
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,f,g,A,B,C,F,G:Point.
(af \mcong{} AF \mwedge{} fb \mcong{} FB \mwedge{} bc \mcong{} BC \mwedge{} ag \mcong{} AG \mwedge{} gc \mcong{} GC) {}\mRightarrow{} fg \mcong{} FG
supposing B(afb) \mwedge{} B(agc) \mwedge{} B(AFB) \mwedge{} B(AGC)
Date html generated:
2020_05_20-AM-09_54_07
Last ObjectModification:
2019_12_23-AM-10_14_48
Theory : euclidean!plane!geometry
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