Nuprl Lemma : isleft-symmetry
∀g:OrientedPlane. ∀a,b:Point. ∀c:{c:Point| a # bc} . isleft(a;b;c) = isleft(b;c;a)
Proof
Definitions occuring in Statement :
geo-isleft: isleft(a;b;c),
oriented-plane: OrientedPlane,
geo-lsep: a # bc,
geo-point: Point,
bool: 𝔹,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
uimplies: b supposing a,
cand: A c∧ B,
and: P ∧ Q,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
oriented-plane: Error :oriented-plane,
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
iff_wf,
assert_wf,
assert-geo-isleft,
geo-left_wf,
left-symmetry,
lsep-all-sym,
geo-lsep_wf,
geo-isleft_wf,
iff_imp_equal_bool
Rules used in proof :
lambdaEquality,
sqequalRule,
instantiate,
applyEquality,
impliesFunctionality,
addLevel,
independent_pairFormation,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
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\} . isleft(a;b;c) = isleft(b;c;a)
Date html generated:
2017_10_02-PM-06_50_20
Last ObjectModification:
2017_08_06-PM-07_30_17
Theory : euclidean!plane!geometry
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