Nuprl Definition : triangle-axiom2
triangle-axiom2(g) == ∀p,q:Point. ∀l,m:Line. ∀s:p ≠ q. ∀s1:l ≠ m. (p ≠ l ⇒ q ≠ m ⇒ p I m ⇒ q I l ⇒ l ∧ m ≠ p ∨ q)
Definitions occuring in Statement :
pgeo-meet: l ∧ m,
pgeo-join: p ∨ q,
pgeo-lsep: l ≠ m,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
pgeo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions occuring in definition :
pgeo-point: Point,
pgeo-line: Line,
pgeo-psep: a ≠ b,
all: ∀x:A. B[x],
pgeo-lsep: l ≠ m,
implies: P ⇒ Q,
pgeo-incident: a I b,
pgeo-plsep: a ≠ b,
pgeo-meet: l ∧ m,
pgeo-join: p ∨ q
FDL editor aliases :
triangle-axiom2
Latex:
triangle-axiom2(g) ==
\mforall{}p,q:Point. \mforall{}l,m:Line. \mforall{}s:p \mneq{} q. \mforall{}s1:l \mneq{} m. (p \mneq{} l {}\mRightarrow{} q \mneq{} m {}\mRightarrow{} p I m {}\mRightarrow{} q I l {}\mRightarrow{} l \mwedge{} m \mneq{} p \mvee{} q)
Date html generated:
2018_05_22-PM-00_40_27
Last ObjectModification:
2017_11_07-AM-11_11_43
Theory : euclidean!plane!geometry
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