Nuprl Lemma : not-assert-isname
∀[L:Cname List]. ∀[z:extd-nameset(L)]. uiff(¬↑isname(z);z ∈ ℕ2)
Proof
Definitions occuring in Statement :
isname: isname(z),
extd-nameset: extd-nameset(L),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
not: ¬A,
implies: P ⇒ Q,
false: False,
extd-nameset: extd-nameset(L),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
isname: isname(z),
rev_uimplies: rev_uimplies(P;Q),
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
btrue: tt,
assert: ↑b,
bfalse: ff,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ
Lemmas referenced :
extd-nameset_subtype_base,
istype-assert,
isname_wf,
istype-void,
int_seg_wf,
extd-nameset_wf,
list_wf,
coordinate_name_wf,
assert_of_le_int,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
int_seg_subtype_special,
int_seg_cases,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
independent_pairFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
thin,
functionIsType,
lambdaEquality_alt,
dependent_functionElimination,
voidElimination,
functionIsTypeImplies,
inhabitedIsType,
because_Cache,
equalityIsType4,
universeIsType,
natural_numberEquality,
imageElimination,
productElimination,
unionElimination,
equalityElimination,
independent_functionElimination,
setElimination,
rename,
independent_isectElimination,
lambdaFormation_alt,
equalityIsType1,
instantiate,
cumulativity,
intEquality,
hypothesis_subsumption,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt
Latex:
\mforall{}[L:Cname List]. \mforall{}[z:extd-nameset(L)]. uiff(\mneg{}\muparrow{}isname(z);z \mmember{} \mBbbN{}2)
Date html generated:
2019_11_05-PM-00_24_08
Last ObjectModification:
2018_11_08-AM-11_41_06
Theory : cubical!sets
Home
Index