Nuprl Lemma : update-context-lvl_wf
∀[ctxt:CubicalContext]. ∀[lvl:ℕ4]. ∀[T:{fst(ctxt) ⊢lvl _}]. ∀[v:varname()].
(update-context-lvl(ctxt;lvl;T;v) ∈ CubicalContext)
Proof
Definitions occuring in Statement :
update-context-lvl: update-context-lvl(ctxt;lvl;T;v),
cubical_context: CubicalContext,
ctt-level-type: {X ⊢lvl _},
varname: varname(),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
pi1: fst(t),
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_context: CubicalContext,
update-context-lvl: update-context-lvl(ctxt;lvl;T;v),
pi1: fst(t),
spreadn: spread3,
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
ctt-level-type: {X ⊢lvl _},
cubical-type: {X ⊢ _},
so_lambda: λ2x.t[x],
true: True,
guard: {T},
so_apply: x[s],
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
varname_wf,
ctt-level-type_wf,
pi1_wf_top,
cubical_set_wf,
int_seg_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,
int_seg_wf,
cubical_context_wf,
cube-context-adjoin_wf-level-type,
cons_wf,
l_member_wf,
ctt-term-meaning_wf,
eq_var_wf,
equal-wf-T-base,
bool_wf,
assert_wf,
equal_wf,
bnot_wf,
not_wf,
istype-assert,
istype-void,
uiff_transitivity,
eqtt_to_assert,
assert-eq_var,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
var-term-meaning_wf,
cons_member,
csm-ap-term-meaning_wf,
cc-fst_wf,
eq_int_wf,
assert_of_eq_int,
subtype_rel_sets,
fset_wf,
nat_wf,
I_cube_wf,
names-hom_wf,
cube-set-restriction_wf,
nh-id_wf,
subtype_rel-equal,
cube-set-restriction-id,
iff_weakening_equal,
nh-comp_wf,
cube-set-restriction-comp,
istype-universe,
subtype_rel_set,
subtype_rel_product,
subtype_rel_dep_function,
subtype_rel_self,
subtype_rel_universe2,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
subtype_rel_universe1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
dependent_pairEquality_alt,
hypothesis,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
instantiate,
independent_pairEquality,
hypothesisEquality,
Error :memTop,
dependent_set_memberEquality_alt,
setElimination,
rename,
imageElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
independent_pairFormation,
voidElimination,
setIsType,
inhabitedIsType,
functionIsType,
because_Cache,
equalityTransitivity,
equalitySymmetry,
baseClosed,
equalityIstype,
lambdaFormation_alt,
equalityElimination,
applyEquality,
productEquality,
functionEquality,
cumulativity,
universeEquality,
spreadEquality,
imageMemberEquality,
productIsType,
promote_hyp,
setEquality
Latex:
\mforall{}[ctxt:CubicalContext]. \mforall{}[lvl:\mBbbN{}4]. \mforall{}[T:\{fst(ctxt) \mvdash{}lvl \_\}]. \mforall{}[v:varname()].
(update-context-lvl(ctxt;lvl;T;v) \mmember{} CubicalContext)
Date html generated:
2020_05_20-PM-08_08_00
Last ObjectModification:
2020_05_04-PM-00_54_48
Theory : cubical!type!theory
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