Nuprl Lemma : filling-op_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. (filling-op(Gamma;A) ∈ 𝕌{[i' | j']})
Proof
Definitions occuring in Statement :
filling-op: filling-op(Gamma;A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
filling-op: filling-op(Gamma;A),
subtype_rel: A ⊆r B,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
and: P ∧ Q,
cubical-path-0: cubical-path-0(Gamma;A;I;i;rho;phi;u),
squash: ↓T,
cubical-type: {X ⊢ _},
subset-iota: iota,
csm-comp: G o F,
csm-ap-type: (AF)s,
compose: f o g,
csm-ap: (s)x,
true: True,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
cubical-type_wf,
cubical_set_wf,
fset_wf,
nat_wf,
not_wf,
fset-member_wf,
int-deq_wf,
istype-nat,
I_cube_wf,
add-name_wf,
face-presheaf_wf2,
cubical-term_wf,
cubical-subset_wf,
cube-set-restriction_wf,
nc-s_wf,
f-subset-add-name,
csm-ap-type_wf,
cubical_set_cumulativity-i-j,
csm-comp_wf,
formal-cube_wf1,
subset-iota_wf,
context-map_wf,
cubical-path-0_wf,
cubical-type-cumulativity2,
istype-void,
cubical-type-at_wf,
equal_wf,
nc-0_wf,
cubical-type-ap-morph_wf,
section-iota_wf,
filling-uniformity_wf,
cubical-type-cumulativity,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
instantiate,
functionEquality,
applyEquality,
lambdaEquality_alt,
cumulativity,
universeEquality,
sqequalRule,
setEquality,
because_Cache,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
lambdaFormation_alt,
setElimination,
rename,
independent_isectElimination,
dependent_functionElimination,
dependent_set_memberEquality_alt,
functionIsType,
productEquality,
imageElimination,
productElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
hyp_replacement,
functionExtensionality,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
voidElimination,
intEquality
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. (filling-op(Gamma;A) \mmember{} \mBbbU{}\{[i' | j']\})
Date html generated:
2020_05_20-PM-03_53_03
Last ObjectModification:
2020_04_09-PM-01_43_28
Theory : cubical!type!theory
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