Nuprl Lemma : pgeo-lsep-or
∀g:BasicProjectivePlane. ∀l,m,n:Line. (l ≠ m ⇒ (l ≠ n ∨ n ≠ m))
Proof
Definitions occuring in Statement :
basic-projective-plane: BasicProjectivePlane,
pgeo-lsep: l ≠ m,
pgeo-line: Line,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
or: P ∨ Q,
basic-projective-plane: BasicProjectivePlane,
member: t ∈ T,
and: P ∧ Q,
exists: ∃x:A. B[x],
pgeo-lsep: l ≠ m,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
pgeo-line_wf,
pgeo-primitives_wf,
projective-plane-structure_wf,
basic-projective-plane_wf,
subtype_rel_transitivity,
basic-projective-plane-subtype,
projective-plane-structure_subtype,
pgeo-lsep_wf,
PL-sep-or,
pgeo-plsep-to-lsep
Rules used in proof :
independent_isectElimination,
instantiate,
because_Cache,
applyEquality,
isectElimination,
inrFormation,
sqequalRule,
unionElimination,
independent_functionElimination,
hypothesisEquality,
rename,
setElimination,
dependent_functionElimination,
extract_by_obid,
introduction,
thin,
productElimination,
sqequalHypSubstitution,
hypothesis,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
inlFormation
Latex:
\mforall{}g:BasicProjectivePlane. \mforall{}l,m,n:Line. (l \mneq{} m {}\mRightarrow{} (l \mneq{} n \mvee{} n \mneq{} m))
Date html generated:
2018_05_22-PM-00_43_16
Last ObjectModification:
2017_11_30-AM-06_49_34
Theory : euclidean!plane!geometry
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