Nuprl Lemma : geo-le-from-be
∀[e:BasicGeometry]. ∀[a,b,c:Point]. |ab| ≤ |ac| supposing B(abc)
Proof
Definitions occuring in Statement :
geo-le: p ≤ q,
geo-length: |s|,
geo-mk-seg: ab,
basic-geometry: BasicGeometry,
geo-between: B(abc),
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
geo-le: p ≤ q,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
geo-ge: ab ≥ cd,
not: ¬A,
implies: P ⇒ Q,
geo-between: B(abc),
and: P ∧ Q,
false: False,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b,c:Point]. |ab| \mleq{} |ac| supposing B(abc)
Date html generated:
2020_05_20-AM-09_53_31
Last ObjectModification:
2019_12_23-AM-08_56_18
Theory : euclidean!plane!geometry
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