Nuprl Lemma : use-triangle-axiom1
∀g:ProjectivePlane. ∀p,q,r:Point. ∀s:p ≠ q. ∀s1:q ≠ r. (r ≠ p ∨ q ⇒ p ≠ q ∨ r)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-join: p ∨ q,
pgeo-psep: a ≠ b,
pgeo-plsep: a ≠ b,
pgeo-point: Point,
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,
and: P ∧ Q,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
pgeo-psep_wf,
pgeo-incident_wf,
pgeo-line_wf,
pgeo-join_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-plsep_wf,
projective-plane-axioms
Rules used in proof :
independent_functionElimination,
productEquality,
because_Cache,
setEquality,
rename,
setElimination,
lambdaEquality,
sqequalRule,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
isectElimination,
productElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p,q,r:Point. \mforall{}s:p \mneq{} q. \mforall{}s1:q \mneq{} r. (r \mneq{} p \mvee{} q {}\mRightarrow{} p \mneq{} q \mvee{} r)
Date html generated:
2018_05_22-PM-00_41_34
Last ObjectModification:
2017_11_28-PM-03_56_49
Theory : euclidean!plane!geometry
Home
Index