Nuprl Lemma : pgeo-leq_transitivity
∀g:ProjectivePlane. ∀l,m,n:Line. (l ≡ m ⇒ m ≡ n ⇒ l ≡ n)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-leq: a ≡ b,
pgeo-line: Line,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
false: False,
pgeo-incident: a I b,
member: t ∈ T,
and: P ∧ Q,
exists: ∃x:A. B[x],
pgeo-lsep: l ≠ m,
not: ¬A,
pgeo-leq: a ≡ b,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
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-leq_wf,
pgeo-lsep_wf,
pgeo-leq-preserves-incidence
Rules used in proof :
independent_isectElimination,
instantiate,
sqequalRule,
applyEquality,
isectElimination,
voidElimination,
because_Cache,
hypothesis,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}l,m,n:Line. (l \mequiv{} m {}\mRightarrow{} m \mequiv{} n {}\mRightarrow{} l \mequiv{} n)
Date html generated:
2018_05_22-PM-00_45_09
Last ObjectModification:
2017_11_28-PM-06_01_25
Theory : euclidean!plane!geometry
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