Nuprl Lemma : geo-left-out-better-1
∀e:EuclideanPlane. ∀a,b,b',p:Point. (p leftof ba ⇒ b' # a ⇒ (¬((¬B(ab'b)) ∧ (¬B(abb')))) ⇒ p leftof b'a)
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-between: B(abc),
geo-left: a leftof bc,
geo-sep: a # b,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-lsep: a # bc,
or: P ∨ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
geo-colinear: Colinear(a;b;c),
not: ¬A,
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
geo-colinear-set: geo-colinear-set(e; L),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
select: L[n],
cons: [a / b],
subtract: n - m,
guard: {T}
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,b',p:Point.
(p leftof ba {}\mRightarrow{} b' \# a {}\mRightarrow{} (\mneg{}((\mneg{}B(ab'b)) \mwedge{} (\mneg{}B(abb')))) {}\mRightarrow{} p leftof b'a)
Date html generated:
2020_05_20-AM-09_56_19
Last ObjectModification:
2019_12_23-PM-08_44_31
Theory : euclidean!plane!geometry
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