Nuprl Lemma : geo-opp-side-sym2
∀e:BasicGeometry. ∀a,b,p,q:Point. (a-pq-b ⇒ a-qp-b)
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 :
guard: {T},
so_apply: x[s],
so_lambda: λ2x.t[x],
basic-geometry: BasicGeometry,
subtype_rel: A ⊆r B,
subtract: n - m,
cons: [a / b],
select: L[n],
true: True,
squash: ↓T,
less_than: a < b,
prop: ℙ,
less_than': less_than'(a;b),
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
top: Top,
l_all: (∀x∈L.P[x]),
geo-colinear-set: geo-colinear-set(e; L),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
geo-colinear: Colinear(a;b;c),
false: False,
member: t ∈ T,
not: ¬A,
and: P ∧ Q,
geo-opp-side: P-AB-Q,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
Error :basic-geo-primitives_wf,
Error :basic-geo-structure_wf,
basic-geometry_wf,
subtype_rel_transitivity,
basic-geometry-subtype,
geo-opp-side_wf,
not_wf,
geo-point_wf,
all_wf,
geo-colinear_wf,
geo-between_wf,
lelt_wf,
false_wf,
length_of_nil_lemma,
length_of_cons_lemma,
geo-between-implies-colinear,
geo-colinear-is-colinear-set
Rules used in proof :
instantiate,
functionEquality,
lambdaEquality,
rename,
setElimination,
applyEquality,
because_Cache,
baseClosed,
imageMemberEquality,
natural_numberEquality,
dependent_set_memberEquality,
voidEquality,
voidElimination,
isect_memberEquality,
sqequalRule,
independent_isectElimination,
isectElimination,
extract_by_obid,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
cut,
independent_functionElimination,
introduction,
promote_hyp,
thin,
productElimination,
independent_pairFormation,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,p,q:Point. (a-pq-b {}\mRightarrow{} a-qp-b)
Date html generated:
2017_10_02-PM-06_22_15
Last ObjectModification:
2017_08_05-PM-04_16_33
Theory : euclidean!plane!geometry
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