Nuprl Lemma : geo-out-strict-colinear
∀e:BasicGeometry. ∀a,b,c:Point. (geo-out-strict(e;a;b;c) ⇒ Colinear(a;b;c))
Proof
Definitions occuring in Statement :
geo-out-strict: geo-out-strict(e;p;a;b),
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-colinear: Colinear(a;b;c),
not: ¬A,
geo-out-strict: geo-out-strict(e;p;a;b),
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
basic-geometry: BasicGeometry,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
guard: {T},
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
false: False,
select: L[n],
cons: [a / b],
subtract: n - m,
subtype_rel: A ⊆r B
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c:Point. (geo-out-strict(e;a;b;c) {}\mRightarrow{} Colinear(a;b;c))
Date html generated:
2020_05_20-AM-09_54_50
Last ObjectModification:
2019_12_23-AM-10_14_41
Theory : euclidean!plane!geometry
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