Nuprl Lemma : assert-geo-isleft
∀g:OrientedPlane. ∀a,b:Point. ∀c:{c:Point| a # bc} .  (↑isleft(a;b;c) 
⇐⇒ a leftof bc)
Proof
Definitions occuring in Statement : 
geo-isleft: isleft(a;b;c)
, 
oriented-plane: OrientedPlane
, 
geo-lsep: a # bc
, 
geo-left: a leftof bc
, 
geo-point: Point
, 
assert: ↑b
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
set: {x:A| B[x]} 
Definitions unfolded in proof : 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
guard: {T}
, 
subtype_rel: A ⊆r B
, 
bfalse: ff
, 
false: False
, 
not: ¬A
, 
uimplies: b supposing a
, 
true: True
, 
btrue: tt
, 
isl: isl(x)
, 
ifthenelse: if b then t else f fi 
, 
assert: ↑b
, 
rev_implies: P 
⇐ Q
, 
and: P ∧ Q
, 
iff: P 
⇐⇒ Q
, 
or: P ∨ Q
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
oriented-plane: Error :oriented-plane, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
geo-isleft: isleft(a;b;c)
, 
all: ∀x:A. B[x]
Lemmas referenced : 
Error :basic-geo-primitives_wf, 
Error :basic-geo-structure_wf, 
basic-geometry-_wf, 
Error :oriented-plane_wf, 
subtype_rel_transitivity, 
Error :oriented-plane-subtype, 
basic-geometry--subtype, 
geo-point_wf, 
set_wf, 
equal_wf, 
btrue_neq_bfalse, 
bfalse_wf, 
assert_elim, 
isl_wf, 
assert_wf, 
geo-left_wf, 
or_wf, 
geo-lsep_wf, 
geo-orientation_wf, 
not-left-and-right
Rules used in proof : 
lambdaEquality, 
instantiate, 
applyEquality, 
dependent_functionElimination, 
voidElimination, 
independent_functionElimination, 
equalitySymmetry, 
equalityTransitivity, 
sqequalRule, 
levelHypothesis, 
independent_isectElimination, 
inrEquality, 
addLevel, 
natural_numberEquality, 
inlEquality, 
voidEquality, 
independent_pairFormation, 
unionElimination, 
because_Cache, 
dependent_set_memberEquality, 
hypothesis, 
hypothesisEquality, 
rename, 
setElimination, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}g:OrientedPlane.  \mforall{}a,b:Point.  \mforall{}c:\{c:Point|  a  \#  bc\}  .    (\muparrow{}isleft(a;b;c)  \mLeftarrow{}{}\mRightarrow{}  a  leftof  bc)
Date html generated:
2017_10_02-PM-06_50_05
Last ObjectModification:
2017_08_06-PM-07_29_51
Theory : euclidean!plane!geometry
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