Nuprl Lemma : pgeo-psep-sym-iff
∀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],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
basic-projective-plane_wf,
projective-plane_wf,
subtype_rel_transitivity,
projective-plane-subtype,
basic-projective-plane-subtype,
projective-plane-structure_subtype,
pgeo-psep_wf,
Error :pgeo-psep-sym
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
hypothesis,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}p,q:Point. (p \mneq{} q \mLeftarrow{}{}\mRightarrow{} q \mneq{} p)
Date html generated:
2018_05_22-PM-00_43_36
Last ObjectModification:
2017_11_21-PM-03_55_32
Theory : euclidean!plane!geometry
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