Nuprl Lemma : geo-colinear-is-colinear-set
∀e:EuclideanPlane. ∀A,B,C:Point. (Colinear(A;B;C) ⇒ geo-colinear-set(e; [A; B; C]))
Proof
Definitions occuring in Statement :
geo-colinear-set: geo-colinear-set(e; L),
euclidean-plane: EuclideanPlane,
geo-colinear: Colinear(a;b;c),
geo-point: Point,
cons: [a / b],
nil: [],
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
euclidean-plane: EuclideanPlane,
member: t ∈ T,
sq_stable: SqStable(P),
squash: ↓T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
select: L[n],
cons: [a / b],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
nat: ℕ,
geo-colinear: Colinear(a;b;c),
not: ¬A,
subtract: n - m,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False
Latex:
\mforall{}e:EuclideanPlane. \mforall{}A,B,C:Point. (Colinear(A;B;C) {}\mRightarrow{} geo-colinear-set(e; [A; B; C]))
Date html generated:
2020_05_20-AM-09_47_35
Last ObjectModification:
2019_11_15-AM-08_32_16
Theory : euclidean!plane!geometry
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