Nuprl Lemma : distinct-triangles_wf
∀pg:ProjectivePlane. ∀t1,t2:pgeo-triangle(pg). (distinct-triangles(pg;t1;t2) ∈ ℙ)
Proof
Definitions occuring in Statement :
pgeo-triangle: pgeo-triangle(pg),
distinct-triangles: distinct-triangles(pg;t1;t2),
projective-plane: ProjectivePlane,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
pi2: snd(t),
pi1: fst(t),
pgeo-triangle: pgeo-triangle(pg),
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
prop: ℙ,
distinct-triangles: distinct-triangles(pg;t1;t2),
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-triangle_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-psep_wf
Rules used in proof :
because_Cache,
productElimination,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
productEquality,
sqequalRule,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}pg:ProjectivePlane. \mforall{}t1,t2:pgeo-triangle(pg). (distinct-triangles(pg;t1;t2) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-PM-00_51_17
Last ObjectModification:
2018_05_14-PM-03_19_35
Theory : euclidean!plane!geometry
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