Nuprl Lemma : update-cubical-context-I_wf
∀[ctxt:CubicalContext]. ∀[v:varname()]. (ctxt,v:I ∈ CubicalContext)
Proof
Definitions occuring in Statement :
update-cubical-context-I: ctxt,v:I,
cubical_context: CubicalContext,
varname: varname(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_context: CubicalContext,
update-cubical-context-I: ctxt,v:I,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
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,
pi1: fst(t),
ctt-level-type: {X ⊢lvl _},
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt
Lemmas referenced :
update-context-lvl_wf,
list_wf,
varname_wf,
l_member_wf,
ctt-term-meaning_wf,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
istype-less_than,
interval-type_wf,
cubical_context_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
introduction,
extract_by_obid,
isectElimination,
sqequalRule,
dependent_pairEquality_alt,
hypothesisEquality,
productIsType,
universeIsType,
hypothesis,
functionIsType,
setIsType,
inhabitedIsType,
because_Cache,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
Error :memTop,
voidElimination,
instantiate
Latex:
\mforall{}[ctxt:CubicalContext]. \mforall{}[v:varname()]. (ctxt,v:I \mmember{} CubicalContext)
Date html generated:
2020_05_20-PM-08_08_40
Last ObjectModification:
2020_05_06-PM-03_26_06
Theory : cubical!type!theory
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