Nuprl Lemma : cubical-subset-I_cube-member
∀[I:fset(ℕ)]. ∀[psi:𝔽(I)]. ∀[J:fset(ℕ)]. ∀[f:I,psi(J)]. ((f ∈ J ⟶ I) ∧ (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,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
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),
name-morph-satisfies: (psi f) = 1
Lemmas referenced :
I_cube_wf,
cubical-subset_wf,
fset_wf,
nat_wf,
face-presheaf_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
setElimination,
thin,
rename,
hypothesisEquality,
hypothesis,
independent_pairFormation,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[psi:\mBbbF{}(I)]. \mforall{}[J:fset(\mBbbN{})]. \mforall{}[f:I,psi(J)]. ((f \mmember{} J {}\mrightarrow{} I) \mwedge{} (psi f) = 1)
Date html generated:
2016_05_18-PM-01_37_00
Last ObjectModification:
2015_12_28-PM-02_59_04
Theory : cubical!type!theory
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