Nuprl Lemma : geo-opp-side-sym
∀e:BasicGeometry. ∀a,b,p,q:Point. (a-pq-b ⇒ b-pq-a)
Proof
Definitions occuring in Statement :
geo-opp-side: P-AB-Q,
basic-geometry: BasicGeometry,
geo-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,
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
basic-geometry: BasicGeometry,
false: False,
not: ¬A,
and: P ∧ Q,
geo-opp-side: P-AB-Q
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-point_wf,
geo-opp-side_wf,
not_wf,
all_wf,
geo-between_wf,
geo-colinear_wf,
geo-between-symmetry
Rules used in proof :
because_Cache,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
functionEquality,
lambdaEquality,
voidElimination,
rename,
setElimination,
dependent_functionElimination,
independent_functionElimination,
promote_hyp,
productElimination,
independent_pairFormation
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,p,q:Point. (a-pq-b {}\mRightarrow{} b-pq-a)
Date html generated:
2017_10_02-PM-06_22_09
Last ObjectModification:
2017_08_05-PM-04_16_29
Theory : euclidean!plane!geometry
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