Nuprl Lemma : sq_stable__geo-non-parallel
∀[g:EuclideanParPlane]. ∀[l:Line]. ∀[L:l,m:Line//l || m]. SqStable(geo-non-parallel(g;l;L))
Proof
Definitions occuring in Statement :
geo-non-parallel: geo-non-parallel(g;l;L),
euclidean-parallel-plane: EuclideanParPlane,
geo-Aparallel: l || m,
geo-line: Line,
quotient: x,y:A//B[x; y],
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
geo-non-parallel: geo-non-parallel(g;l;L),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
so_apply: x[s],
exists: ∃x:A. B[x],
sq_stable: SqStable(P),
squash: ↓T,
guard: {T}
Lemmas referenced :
sq_stable__squash,
all_wf,
equal_wf,
quotient_wf,
geo-Aparallel_wf,
euclidean-planes-subtype,
geoline-subtype1,
geo-Aparallel-equiv,
subtype_quotient,
geo-line_wf,
exists_wf,
geo-point_wf,
geo-incident_wf,
squash_wf,
geo-non-parallel_wf,
euclidean-plane-structure-subtype,
subtype_rel_transitivity,
euclidean-parallel-plane_wf,
euclidean-plane-structure_wf,
geo-primitives_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
sqequalRule,
lambdaEquality,
functionEquality,
hypothesisEquality,
applyEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
productEquality,
imageElimination,
imageMemberEquality,
baseClosed,
instantiate,
isect_memberEquality
Latex:
\mforall{}[g:EuclideanParPlane]. \mforall{}[l:Line]. \mforall{}[L:l,m:Line//l || m]. SqStable(geo-non-parallel(g;l;L))
Date html generated:
2018_05_22-PM-01_12_33
Last ObjectModification:
2018_05_11-PM-01_16_17
Theory : euclidean!plane!geometry
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