Nuprl Lemma : pgeo-psep-sym
∀g:ProjectivePlane. ∀p,q:Point. (p ≠ q ⇒ q ≠ p)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-psep: 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,
exists: ∃x:A. B[x],
pgeo-psep: a ≠ b,
implies: P ⇒ Q,
all: ∀x:A. B[x],
cand: A c∧ B
Lemmas referenced :
pgeo-point_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,
plsep-implies-ptriangle,
pgeo-incident_wf,
pgeo-line_wf,
pgeo-join_wf,
pgeo-plsep-to-lsep,
pgeo-plsep-to-psep,
incident-join-second,
use-triangle-axiom2,
plsep-join-implies,
incident-join-first,
projective-plane-subtype-basic,
pgeo-meet-implies-plsep
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
independent_functionElimination,
hypothesisEquality,
dependent_functionElimination,
extract_by_obid,
introduction,
rename,
thin,
productElimination,
sqequalHypSubstitution,
hypothesis,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
productEquality,
setEquality,
setElimination,
lambdaEquality,
independent_pairFormation
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p,q:Point. (p \mneq{} q {}\mRightarrow{} q \mneq{} p)
Date html generated:
2018_05_22-PM-00_42_37
Last ObjectModification:
2017_11_30-AM-10_34_11
Theory : euclidean!plane!geometry
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