Nuprl Lemma : geo-colinear-same
∀[e:BasicGeometry]. ∀[a,b:Point]. (Colinear(a;b;b) ∧ Colinear(b;a;b) ∧ Colinear(b;b;a))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-colinear: Colinear(a;b;c),
geo-point: Point,
uall: ∀[x:A]. B[x],
and: P ∧ Q
Definitions unfolded in proof :
guard: {T},
subtract: n - m,
cons: [a / b],
select: L[n],
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
lelt: i ≤ j < k,
int_seg: {i..j-},
top: Top,
l_all: (∀x∈L.P[x]),
geo-colinear-set: geo-colinear-set(e; L),
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
not: ¬A,
geo-colinear: Colinear(a;b;c),
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[e:BasicGeometry]. \mforall{}[a,b:Point]. (Colinear(a;b;b) \mwedge{} Colinear(b;a;b) \mwedge{} Colinear(b;b;a))
Date html generated:
2020_05_20-AM-09_48_56
Last ObjectModification:
2019_12_20-PM-07_37_53
Theory : euclidean!plane!geometry
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