Nuprl Lemma : geo-intersect-irreflexive
∀[g:EuclideanPlane]. ∀[m:LINE]. (¬m \/ m)
Proof
Definitions occuring in Statement :
geo-intersect: L \/ M,
geoline: LINE,
euclidean-plane: EuclideanPlane,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
exists: ∃x:A. B[x],
and: P ∧ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
basic-geometry-: BasicGeometry-,
geo-line: Line,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
uiff: uiff(P;Q),
cand: A c∧ B,
pi1: fst(t),
pi2: snd(t),
geoline: LINE,
quotient: x,y:A//B[x; y],
rev_implies: P ⇐ Q
Lemmas referenced :
geo-intersect_wf,
geoline_wf,
euclidean-plane_wf,
geo-intersect-iff2,
geo-strict-between-sep1,
geo-line-eq-geoline,
geo-sep_wf,
euclidean-plane-structure-subtype,
euclidean-plane-subtype,
subtype_rel_transitivity,
euclidean-plane-structure_wf,
geo-primitives_wf,
geo-point_wf,
geo-line-eq-to-col,
member_wf,
geo-line_wf,
geo-line-eq_wf,
not-lsep-iff-colinear,
lsep-all-sym2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
because_Cache,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
isect_memberEquality,
productElimination,
rename,
dependent_pairEquality,
applyEquality,
instantiate,
independent_isectElimination,
productEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
pertypeElimination
Latex:
\mforall{}[g:EuclideanPlane]. \mforall{}[m:LINE]. (\mneg{}m \mbackslash{}/ m)
Date html generated:
2018_05_22-PM-01_06_47
Last ObjectModification:
2018_05_10-PM-06_26_16
Theory : euclidean!plane!geometry
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