Nuprl Lemma : pgeo-leq-preserves-plsep
∀g:ProjectivePlane. ∀a:Point. ∀l,m:Line. (a ≠ l ⇒ l ≡ m ⇒ a ≠ m)
Proof
Definitions occuring in Statement :
projective-plane: ProjectivePlane,
pgeo-leq: a ≡ b,
pgeo-plsep: a ≠ b,
pgeo-line: Line,
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,
false: False,
not: ¬A,
pgeo-leq: a ≡ b,
or: P ∨ Q,
projective-plane: ProjectivePlane,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-point_wf,
pgeo-line_wf,
pgeo-plsep_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-leq_wf,
PL-sep-or
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
isectElimination,
voidElimination,
unionElimination,
independent_functionElimination,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}g:ProjectivePlane. \mforall{}a:Point. \mforall{}l,m:Line. (a \mneq{} l {}\mRightarrow{} l \mequiv{} m {}\mRightarrow{} a \mneq{} m)
Date html generated:
2018_05_22-PM-00_44_26
Last ObjectModification:
2017_11_17-PM-02_51_35
Theory : euclidean!plane!geometry
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