Nuprl Lemma : h-level_wf
∀[n:ℕ]. ∀[X:j⊢]. ∀[A:{X ⊢ _}]. X ⊢ h-level(X;n;A)
Proof
Definitions occuring in Statement :
h-level: h-level(X;n;A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ,
h-level: h-level(X;n;A),
lt_int: i <z j,
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
subtype_rel: A ⊆r B,
sq_type: SQType(T),
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
or: P ∨ Q,
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
primrec-unroll,
subtract-1-ge-0,
istype-nat,
contractible-type_wf,
cubical-type_wf,
cubical_set_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eq_int_eq_false_intro,
intformeq_wf,
int_formula_prop_eq_lemma,
int_subtype_base,
bfalse_wf,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
cubical-pi_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm-ap-type_wf,
cc-fst_wf,
path-type_wf,
csm-ap-term_wf,
cc-snd_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
isect_memberEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
functionIsTypeImplies,
because_Cache,
instantiate,
cumulativity,
equalityIstype,
applyEquality,
baseClosed,
sqequalBase,
closedConclusion,
unionElimination,
equalityElimination,
productElimination,
promote_hyp
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. X \mvdash{} h-level(X;n;A)
Date html generated:
2020_05_20-PM-03_35_02
Last ObjectModification:
2020_04_06-PM-07_00_21
Theory : cubical!type!theory
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