Nuprl Lemma : subtype-face-presheaf-point
∀[I:fset(ℕ)]. (Point(face_lattice(I)) ⊆r 𝔽(I))
Proof
Definitions occuring in Statement :
face-presheaf: 𝔽,
face_lattice: face_lattice(I),
I_cube: A(I),
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-point: Point(l),
record-select: r.x,
face_lattice: face_lattice(I),
face-lattice: face-lattice(T;eq),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
I_cube: A(I),
functor-ob: functor-ob(F),
pi1: fst(t),
face-presheaf: 𝔽,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_self,
fset_wf,
names_wf,
assert_wf,
fset-antichain_wf,
union-deq_wf,
names-deq_wf,
fset-all_wf,
fset-contains-none_wf,
face-lattice-constraints_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
unionEquality,
hypothesisEquality,
hypothesis,
because_Cache,
productEquality,
lambdaEquality,
axiomEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. (Point(face\_lattice(I)) \msubseteq{}r \mBbbF{}(I))
Date html generated:
2016_05_18-PM-00_16_23
Last ObjectModification:
2015_12_28-PM-02_59_56
Theory : cubical!type!theory
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