Nuprl Lemma : update-cubical-context_wf
∀[ctxt:CubicalContext]. ∀[v:varname()]. ∀[T:Provisional''''(lvl:ℕ4 × {fst(ctxt) ⊢lvl _})].
(ctxt; v:T ∈ ?CubicalContext)
Proof
Definitions occuring in Statement :
update-cubical-context: ctxt; v:T,
cubical-context: ?CubicalContext,
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,
product: x:A × B[x],
natural_number: $n,
provisional-type: Provisional(T)
Definitions unfolded in proof :
cubical-context: ?CubicalContext,
uall: ∀[x:A]. B[x],
member: t ∈ T,
update-cubical-context: ctxt; v:T,
cubical_context: CubicalContext,
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,
pi1: fst(t)
Lemmas referenced :
int_seg_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,
cubical_context_wf,
update-context-lvl_wf,
l_member_wf,
varname_wf,
ctt-term-meaning_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
productEquality,
natural_numberEquality,
hypothesis,
productElimination,
independent_pairEquality,
hypothesisEquality,
Error :memTop,
dependent_set_memberEquality_alt,
setElimination,
rename,
imageElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
sqequalRule,
independent_pairFormation,
universeIsType,
voidElimination,
isect_memberEquality_alt,
inhabitedIsType,
lambdaFormation_alt,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_pairEquality_alt,
functionIsType,
setIsType,
productIsType
Latex:
\mforall{}[ctxt:CubicalContext]. \mforall{}[v:varname()]. \mforall{}[T:Provisional''''(lvl:\mBbbN{}4 \mtimes{} \{fst(ctxt) \mvdash{}lvl \_\})].
(ctxt; v:T \mmember{} ?CubicalContext)
Date html generated:
2020_05_20-PM-08_09_59
Last ObjectModification:
2020_05_04-PM-01_13_34
Theory : cubical!type!theory
Home
Index