Nuprl Lemma : member-cubical-subset-I_cube
∀[I:fset(ℕ)]. ∀[psi:𝔽(I)]. ∀[J:fset(ℕ)]. ∀[f:J ⟶ I]. f ∈ I,psi(J) supposing (psi f) = 1
Proof
Definitions occuring in Statement :
cubical-subset: I,psi,
name-morph-satisfies: (psi f) = 1,
face-presheaf: 𝔽,
I_cube: A(I),
names-hom: I ⟶ J,
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cubical-subset: I,psi,
I_cube: A(I),
names-cat: NamesCat,
rep-sub-sheaf: rep-sub-sheaf(C;X;P),
functor-ob: functor-ob(F),
pi1: fst(t),
cat-arrow: cat-arrow(C),
pi2: snd(t),
subtype_rel: A ⊆r B,
face-presheaf: 𝔽,
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,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
name-morph-satisfies_wf,
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,
names-hom_wf,
nat_wf,
I_cube_wf,
face-presheaf_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
hypothesisEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setEquality,
unionEquality,
because_Cache,
productEquality,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[psi:\mBbbF{}(I)]. \mforall{}[J:fset(\mBbbN{})]. \mforall{}[f:J {}\mrightarrow{} I]. f \mmember{} I,psi(J) supposing (psi f) = 1
Date html generated:
2016_05_18-PM-01_36_54
Last ObjectModification:
2015_12_28-PM-02_59_27
Theory : cubical!type!theory
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