Nuprl Lemma : ulist-ext
∀[T:Type]. ulist(T) ≡ T List
Proof
Definitions occuring in Statement :
ulist: ulist(T),
list: T List,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
ulist: ulist(T),
urec: urec(F),
tunion: ⋃x:A.B[x],
pi2: snd(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],
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
compose: f o g,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
so_apply: x[s],
so_lambda: λ2x.t[x],
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
b-union: A ⋃ B
Lemmas referenced :
istype-universe,
ulist_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
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,
fun_exp0_lemma,
subtract-1-ge-0,
list-ext,
subtype_rel_transitivity,
fun_exp_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
istype-le,
b-union_wf,
unit_wf2,
list_wf,
fun_exp_unroll,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
intformeq_wf,
int_formula_prop_eq_lemma,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
equal_wf,
le_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
satisfiable-full-omega-tt,
subtract_wf,
subtype_rel_wf,
subtype_rel_product,
subtype_rel_self,
subtype_rel_b-union,
list-cases,
product_subtype_list,
colength-cons-not-zero,
colength_wf_list,
set_subtype_base,
int_subtype_base,
spread_cons_lemma,
decidable__equal_int,
itermAdd_wf,
int_term_value_add_lemma,
istype-nat,
ifthenelse_wf,
btrue_wf,
fun_exp1_lemma,
false_wf,
bfalse_wf,
subtype_urec,
continuous'-monotone-bunion,
continuous'-monotone-constant,
continuous'-monotone-product,
continuous'-monotone-identity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
axiomEquality,
hypothesis,
instantiate,
extract_by_obid,
isectElimination,
universeEquality,
lambdaEquality_alt,
imageElimination,
hypothesisEquality,
applyEquality,
universeIsType,
setElimination,
rename,
intWeakElimination,
lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
functionIsTypeImplies,
inhabitedIsType,
voidEquality,
lambdaEquality,
dependent_set_memberEquality_alt,
unionElimination,
productEquality,
because_Cache,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
equalityIstype,
promote_hyp,
cumulativity,
lambdaFormation,
computeAll,
isect_memberEquality,
intEquality,
dependent_pairFormation,
dependent_set_memberEquality,
hypothesis_subsumption,
applyLambdaEquality,
baseApply,
closedConclusion,
baseClosed,
sqequalBase,
dependent_pairEquality,
imageMemberEquality
Latex:
\mforall{}[T:Type]. ulist(T) \mequiv{} T List
Date html generated:
2019_10_15-AM-11_32_14
Last ObjectModification:
2019_06_26-PM-03_58_07
Theory : general
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