Nuprl Lemma : circle-strict-overlap-implies-overlap
∀g:GeometryPrimitives. (BasicGeometryAxioms(g) ⇒ (∀a,b,c,d:Point. (StrictOverlap(a;b;c;d) ⇒ Overlap(a;b;c;d))))
Proof
Definitions occuring in Statement :
circle-strict-overlap: StrictOverlap(a;b;c;d),
circle-overlap: Overlap(a;b;c;d),
basic-geo-axioms: BasicGeometryAxioms(g),
geo-primitives: GeometryPrimitives,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
circle-strict-overlap: StrictOverlap(a;b;c;d),
circle-overlap: Overlap(a;b;c;d),
squash: ↓T,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
basic-geo-axioms: BasicGeometryAxioms(g)
Latex:
\mforall{}g:GeometryPrimitives
(BasicGeometryAxioms(g) {}\mRightarrow{} (\mforall{}a,b,c,d:Point. (StrictOverlap(a;b;c;d) {}\mRightarrow{} Overlap(a;b;c;d))))
Date html generated:
2020_05_20-AM-09_43_46
Last ObjectModification:
2019_11_13-PM-01_56_24
Theory : euclidean!plane!geometry
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