Nuprl Lemma : pgeo-non-trivial-dual
∀g:ProjectivePlane. (∃l:Line [l ≡ l])
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-leq: a ≡ b,
pgeo-line: Line,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]]
Definitions unfolded in proof :
prop: ℙ,
implies: P ⇒ Q,
sq_exists: ∃x:A [B[x]],
uimplies: b supposing a,
guard: {T},
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
projective-plane: ProjectivePlane,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-primitives_wf,
projective-plane-structure_subtype,
pgeo-leq_wf,
pgeo-leq_weakening,
projective-plane-structure_wf,
projective-plane-structure-complete_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
projective-plane-structure-complete_subtype,
pgeo-three-lines-axiom,
pgeo-non-trivial
Rules used in proof :
independent_functionElimination,
because_Cache,
dependent_set_memberEquality,
sqequalRule,
independent_isectElimination,
isectElimination,
instantiate,
applyEquality,
productElimination,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. (\mexists{}l:Line [l \mequiv{} l])
Date html generated:
2018_05_22-PM-00_47_39
Last ObjectModification:
2017_11_27-PM-04_31_35
Theory : euclidean!plane!geometry
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