Nuprl Lemma : geo-between-same-side
∀e:BasicGeometry. ∀[A,B,C,D:Point]. (¬((¬B(ACD)) ∧ (¬B(ADC)))) supposing (A # B and B(ABC) and B(ABD))
Proof
Definitions occuring in Statement :
basic-geometry: BasicGeometry,
geo-between: B(abc),
geo-sep: a # b,
geo-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ,
basic-geometry: BasicGeometry,
exists: ∃x:A. B[x],
geo-eq: a ≡ b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
euclidean-plane: EuclideanPlane,
basic-geometry-: BasicGeometry-,
uiff: uiff(P;Q),
squash: ↓T,
true: True,
subtract: n - m,
cons: [a / b],
select: L[n],
satisfiable_int_formula: satisfiable_int_formula(fmla),
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),
so_apply: x[s1;s2;s3],
so_lambda: so_lambda3,
append: as @ bs,
ge: i ≥ j ,
less_than: a < b,
cand: A c∧ B,
less_than': less_than'(a;b),
le: A ≤ B,
nat: ℕ,
l_member: (x ∈ l),
stable: Stable{P}
Latex:
\mforall{}e:BasicGeometry
\mforall{}[A,B,C,D:Point]. (\mneg{}((\mneg{}B(ACD)) \mwedge{} (\mneg{}B(ADC)))) supposing (A \# B and B(ABC) and B(ABD))
Date html generated:
2020_05_20-AM-09_53_03
Last ObjectModification:
2020_01_27-PM-10_02_49
Theory : euclidean!plane!geometry
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