Nuprl Lemma : incident-join-first
∀g:ProjectivePlaneStructure. ∀p,q:Point. ∀s:p ≠ q. p I p ∨ q
Proof
Definitions occuring in Statement :
pgeo-join: p ∨ q,
projective-plane-structure: ProjectivePlaneStructure,
pgeo-psep: a ≠ b,
pgeo-incident: a I b,
pgeo-point: Point,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
and: P ∧ Q,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
pgeo-join_wf,
set_wf,
pgeo-line_wf,
pgeo-incident_wf,
sq_stable__pgeo-incident,
projective-plane-structure_subtype,
equal_wf,
pgeo-psep_wf,
pgeo-point_wf,
projective-plane-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
productEquality,
setElimination,
rename,
productElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}g:ProjectivePlaneStructure. \mforall{}p,q:Point. \mforall{}s:p \mneq{} q. p I p \mvee{} q
Date html generated:
2018_05_22-PM-00_35_11
Last ObjectModification:
2017_10_30-PM-09_42_51
Theory : euclidean!plane!geometry
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