Nuprl Lemma : geo-out_weakening
∀e:BasicGeometry. ∀a,b,c:Point. (a # b ⇒ b ≡ c ⇒ out(a bc))
Proof
Definitions occuring in Statement :
geo-out: out(p ab),
basic-geometry: BasicGeometry,
geo-eq: a ≡ b,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-out: out(p ab),
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
guard: {T}
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (a \# b {}\mRightarrow{} b \mequiv{} c {}\mRightarrow{} out(a bc))
Date html generated:
2020_05_20-AM-09_54_57
Last ObjectModification:
2020_01_13-PM-03_29_25
Theory : euclidean!plane!geometry
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