Nuprl Lemma : nat-star-retract_wf
∀[s:ℕ ⟶ ℕ]. (nat-star-retract(s) ∈ ℕ*)
Proof
Definitions occuring in Statement :
nat-star-retract: nat-star-retract(s),
nat-star: ℕ*,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
cand: A c∧ B,
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat-star-retract: nat-star-retract(s),
nat: ℕ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
guard: {T},
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
nat-star: ℕ*
Lemmas referenced :
nat_properties,
decidable__equal_int,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
l_exists_iff,
member_upto2,
decidable__lt,
bl-exists_wf,
int_seg_wf,
upto_wf,
l_member_wf,
lt_int_wf,
nat_wf,
int_seg_subtype_nat,
istype-false,
eqtt_to_assert,
assert-bl-exists,
l_exists_functionality,
assert_wf,
less_than_wf,
iff_weakening_uiff,
subtype_rel_set,
assert_of_lt_int,
le_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
l_exists_wf,
istype-int,
set_subtype_base,
int_subtype_base
Rules used in proof :
approximateComputation,
int_eqEquality,
Error :isect_memberEquality_alt,
Error :productIsType,
imageElimination,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
Error :lambdaFormation_alt,
hypothesisEquality,
Error :universeIsType,
applyEquality,
functionExtensionality,
independent_isectElimination,
independent_pairFormation,
Error :setIsType,
Error :inhabitedIsType,
unionElimination,
equalityElimination,
productElimination,
dependent_functionElimination,
independent_functionElimination,
Error :dependent_set_memberEquality_alt,
equalityTransitivity,
equalitySymmetry,
Error :dependent_pairFormation_alt,
Error :equalityIsType1,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
Error :functionIsType,
Error :equalityIsType4,
intEquality,
axiomEquality
Latex:
\mforall{}[s:\mBbbN{} {}\mrightarrow{} \mBbbN{}]. (nat-star-retract(s) \mmember{} \mBbbN{}*)
Date html generated:
2019_06_20-PM-03_17_41
Last ObjectModification:
2019_06_20-PM-03_12_51
Theory : continuity
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