Nuprl Lemma : not-left-and-right
∀g:EuclideanPlane. ∀a,b,c:Point. (a leftof bc ⇒ (¬a leftof cb))
Proof
Definitions occuring in Statement :
euclidean-plane: EuclideanPlane,
geo-left: a leftof bc,
geo-point: Point,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
euclidean-plane: EuclideanPlane,
exists: ∃x:A. B[x],
and: P ∧ Q,
iff: 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,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
select: L[n],
cons: [a / b],
subtract: n - m
Latex:
\mforall{}g:EuclideanPlane. \mforall{}a,b,c:Point. (a leftof bc {}\mRightarrow{} (\mneg{}a leftof cb))
Date html generated:
2020_05_20-AM-09_48_14
Last ObjectModification:
2019_11_13-PM-03_29_09
Theory : euclidean!plane!geometry
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