Nuprl Lemma : geo-sep-O-X
∀e:EuclideanPlaneStructure. O ≠ X
Proof
Definitions occuring in Statement :
geo-X: X,
geo-O: O,
euclidean-plane-structure: EuclideanPlaneStructure,
geo-sep: a ≠ b,
all: ∀x:A. B[x]
Definitions unfolded in proof :
implies: P ⇒ Q,
prop: ℙ,
exists: ∃x:A. B[x],
sq_exists: ∃x:{A| B[x]},
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-O: O,
geo-X: X,
all: ∀x:A. B[x],
squash: ↓T,
sq_stable: SqStable(P),
pi2: snd(t),
pi1: fst(t)
Lemmas referenced :
euclidean-plane-structure_wf,
equal_wf,
geo-sep_wf,
sq_exists_wf,
euclidean-plane-structure-subtype,
geo-point_wf,
exists_wf,
geo-nontrivial_wf,
sq_stable__geo-sep
Rules used in proof :
independent_functionElimination,
dependent_functionElimination,
equalitySymmetry,
equalityTransitivity,
because_Cache,
lambdaEquality,
sqequalRule,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
imageElimination,
baseClosed,
imageMemberEquality,
rename,
setElimination,
productElimination
Latex:
\mforall{}e:EuclideanPlaneStructure. O \mneq{} X
Date html generated:
2017_10_02-PM-03_28_30
Last ObjectModification:
2017_08_04-PM-08_50_39
Theory : euclidean!plane!geometry
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