Nuprl Lemma : geo-intersect-symmetry
∀e:EuclideanPlane. ∀l,m:LINE. (l \/ m ⇒ m \/ l)
Proof
Definitions occuring in Statement :
geo-intersect: L \/ M,
geoline: LINE,
euclidean-plane: EuclideanPlane,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
exists: ∃x:A. B[x],
rev_implies: P ⇐ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
geo-strict-between: a-b-c,
cand: A c∧ B
Lemmas referenced :
geo-intersect-iff2,
geo-strict-between_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-incident_wf,
geo-left_wf,
exists_wf,
geo-point_wf,
geo-intersect_wf,
geoline_wf,
geo-between-symmetry,
geo-sep-sym
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
dependent_pairFormation,
independent_pairFormation,
productEquality,
isectElimination,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
lambdaEquality
Latex:
\mforall{}e:EuclideanPlane. \mforall{}l,m:LINE. (l \mbackslash{}/ m {}\mRightarrow{} m \mbackslash{}/ l)
Date html generated:
2018_05_22-PM-01_06_34
Last ObjectModification:
2018_05_10-PM-06_10_09
Theory : euclidean!plane!geometry
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