Nuprl Lemma : point-sep-from-line-triangle_wf
∀g:ProjectivePlane. ∀p:Point. ∀l,m,n:Line. (p ≠ LΔ(l;m;n) ∈ ℙ)
Proof
Definitions occuring in Statement :
point-sep-from-line-triangle: p ≠ LΔ(l;m;n),
projective-plane: ProjectivePlane,
pgeo-line: Line,
pgeo-point: Point,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
point-sep-from-line-triangle: p ≠ LΔ(l;m;n),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
line-triangle_wf,
pgeo-plsep_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,
all_wf
Rules used in proof :
dependent_functionElimination,
productEquality,
because_Cache,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p:Point. \mforall{}l,m,n:Line. (p \mneq{} L\mDelta{}(l;m;n) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_50_02
Last ObjectModification:
2017_12_01-PM-03_05_42
Theory : euclidean!plane!geometry
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