Nuprl Lemma : geo-isleft_wf
∀[g:EuclideanPlaneStructure]. ∀[a,b:Point]. ∀[c:{c:Point| a # bc} ]. (isleft(a;b;c) ∈ 𝔹)
Proof
Definitions occuring in Statement :
geo-isleft: isleft(a;b;c),
euclidean-plane-structure: EuclideanPlaneStructure,
geo-lsep: a # bc,
geo-point: Point,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
geo-isleft: isleft(a;b;c),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
euclidean-plane-structure_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
set_wf,
geo-lsep_wf,
geo-orientation_wf,
geo-left_wf,
isl_wf
Rules used in proof :
isect_memberEquality,
lambdaEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_set_memberEquality,
hypothesis,
because_Cache,
applyEquality,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
rename,
thin,
setElimination,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:EuclideanPlaneStructure]. \mforall{}[a,b:Point]. \mforall{}[c:\{c:Point| a \# bc\} ]. (isleft(a;b;c) \mmember{} \mBbbB{})
Date html generated:
2017_10_02-PM-06_49_58
Last ObjectModification:
2017_08_06-PM-07_38_28
Theory : euclidean!plane!geometry
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