Nuprl Lemma : trivial-section_wf
∀[I:fset(ℕ)]. ∀[X:Top]. ∀[phi:Point(face_lattice(I))]. () ∈ {I,phi ⊢ _:X} supposing phi = 0 ∈ Point(face_lattice(I))
Proof
Definitions occuring in Statement :
trivial-section: (),
cubical-term: {X ⊢ _:A},
cubical-subset: I,psi,
face_lattice: face_lattice(I),
lattice-0: 0,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
cubical-term: {X ⊢ _:A},
subtype_rel: A ⊆r B,
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: ob(F),
pi1: fst(t),
face-presheaf: 𝔽,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
name-morph-satisfies: (psi f) = 1,
bdd-distributive-lattice: BoundedDistributiveLattice,
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
all: ∀x:A. B[x]
Lemmas referenced :
cubical-subset-I_cube-member,
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,
equal_wf,
lattice-point_wf,
face_lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
lattice-meet_wf,
lattice-join_wf,
fl-morph_wf,
bounded-lattice-hom_wf,
bdd-distributive-lattice_wf,
squash_wf,
true_wf,
fl-morph-0,
iff_weakening_equal,
face-lattice-0-not-1,
I_cube_wf,
cubical-subset_wf,
nat_wf,
lattice-1_wf,
names-hom_wf,
lattice-0_wf,
top_wf,
all_wf,
cubical-type-at_wf,
cube-set-restriction_wf,
cubical-type-ap-morph_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
functionExtensionality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
setEquality,
unionEquality,
because_Cache,
hypothesis,
productEquality,
lambdaEquality,
productElimination,
equalitySymmetry,
hyp_replacement,
applyLambdaEquality,
instantiate,
cumulativity,
universeEquality,
independent_isectElimination,
setElimination,
rename,
equalityTransitivity,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
voidElimination,
lambdaFormation,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[X:Top]. \mforall{}[phi:Point(face\_lattice(I))]. () \mmember{} \{I,phi \mvdash{} \_:X\} supposing phi = 0
Date html generated:
2017_10_05-AM-01_22_48
Last ObjectModification:
2017_07_28-AM-09_35_01
Theory : cubical!type!theory
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