Nuprl Lemma : geo-tar-opp-side-symmetry
∀e:BasicGeometry. ∀a,b,c,d:Point. (geo-tar-opp-side(e;a;b;c;d) ⇒ geo-tar-opp-side(e;b;a;c;d))
Proof
Definitions occuring in Statement :
geo-tar-opp-side: geo-tar-opp-side(e;a;b;p;q),
basic-geometry: BasicGeometry,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
subtype_rel: A ⊆r B,
basic-geometry: BasicGeometry,
prop: ℙ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
exists: ∃x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
geo-tar-opp-side: geo-tar-opp-side(e;a;b;p;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-point_wf,
geo-tar-opp-side_wf,
geo-between_wf,
geo-colinear_wf,
geo-between-symmetry
Rules used in proof :
instantiate,
sqequalRule,
because_Cache,
applyEquality,
rename,
setElimination,
productEquality,
independent_isectElimination,
isectElimination,
dependent_functionElimination,
extract_by_obid,
introduction,
hypothesisEquality,
dependent_pairFormation,
independent_pairFormation,
hypothesis,
cut,
thin,
productElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}e:BasicGeometry. \mforall{}a,b,c,d:Point. (geo-tar-opp-side(e;a;b;c;d) {}\mRightarrow{} geo-tar-opp-side(e;b;a;c;d))
Date html generated:
2017_10_02-PM-06_23_25
Last ObjectModification:
2017_08_05-PM-04_17_36
Theory : euclidean!plane!geometry
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