Nuprl Lemma : pgeo-plsep-class_wf
∀[g:ProjectivePlane]. ∀[pc:PointClass]. ∀[lc:LineClass]. (pc # lc ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-plsep-class: pc # lc,
pgeo-line-class: LineClass,
pgeo-point-class: PointClass,
projective-plane: ProjectivePlane,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
pgeo-line-class: LineClass,
all: ∀x:A. B[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
pgeo-point-class: PointClass,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
pgeo-plsep-class: pc # lc,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
pgeo-plsep_wf,
pgeo-leq-equiv,
pgeo-leq_wf,
pgeo-line-class_wf,
pgeo-peq-equiv,
pgeo-peq_wf,
subtype_quotient,
pgeo-point-class_wf,
equal_wf,
pgeo-line_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
projective-plane-structure_subtype,
pgeo-point_wf,
exists_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
productEquality,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[g:ProjectivePlane]. \mforall{}[pc:PointClass]. \mforall{}[lc:LineClass]. (pc \# lc \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_56_44
Last ObjectModification:
2018_01_03-PM-03_50_35
Theory : euclidean!plane!geometry
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