Nuprl Lemma : geo-colinear-implies
∀e:BasicGeometry-. ∀a,b,c:Point. (Colinear(a;b;c) ⇒ (¬((¬B(abc)) ∧ (¬B(bca)) ∧ (¬B(cab)))))
Proof
Definitions occuring in Statement :
basic-geometry-: BasicGeometry-,
geo-colinear: Colinear(a;b;c),
geo-between: B(abc),
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
basic-geometry-: BasicGeometry-,
euclidean-plane: EuclideanPlane,
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
geo-colinear: Colinear(a;b;c),
not: ¬A,
false: False,
geo-between: B(abc),
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
or: P ∨ Q,
iff: P ⇐⇒ Q,
cand: A c∧ B
Latex:
\mforall{}e:BasicGeometry-. \mforall{}a,b,c:Point. (Colinear(a;b;c) {}\mRightarrow{} (\mneg{}((\mneg{}B(abc)) \mwedge{} (\mneg{}B(bca)) \mwedge{} (\mneg{}B(cab)))))
Date html generated:
2020_05_20-AM-09_48_28
Last ObjectModification:
2020_01_27-PM-07_08_50
Theory : euclidean!plane!geometry
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