Nuprl Lemma : geo-not-triangle
∀e:HeytingGeometry. ∀a,b,c:Point. ((¬a # bc) ⇒ (¬((¬B(abc)) ∧ (¬B(bca)) ∧ (¬B(cab)))))
Proof
Definitions occuring in Statement :
geo-triangle: a # bc,
heyting-geometry: HeytingGeometry,
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],
implies: P ⇒ Q,
not: ¬A,
false: False,
member: t ∈ T,
heyting-geometry: HeytingGeometry,
geo-colinear: Colinear(a;b;c),
geo-lsep: a # bc,
or: P ∨ Q,
geo-triangle: a # bc,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
stable: Stable{P}
Latex:
\mforall{}e:HeytingGeometry. \mforall{}a,b,c:Point. ((\mneg{}a \# bc) {}\mRightarrow{} (\mneg{}((\mneg{}B(abc)) \mwedge{} (\mneg{}B(bca)) \mwedge{} (\mneg{}B(cab)))))
Date html generated:
2020_05_20-AM-10_32_39
Last ObjectModification:
2019_12_28-AM-08_24_20
Theory : euclidean!plane!geometry
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