Nuprl Lemma : enum-fin-seq-max2_wf
∀[M:n:ℕ ⟶ (ℕn ⟶ 𝔹) ⟶ (ℕ?)]. ∀[m:ℕ]. (enum-fin-seq-max2(M;m) ∈ ℕ)
Proof
Definitions occuring in Statement :
enum-fin-seq-max2: enum-fin-seq-max2(M;m),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
enum-fin-seq-max2: enum-fin-seq-max2(M;m),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
squash: ↓T,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
less_than: a < b,
less_than': less_than'(a;b),
true: True,
le: A ≤ B,
false: False,
not: ¬A,
list_n: A List(n),
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
cand: A c∧ B,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
imax-list_wf,
map_wf,
nat_wf,
bool_wf,
equal_wf,
enum-fin-seq_wf,
map-length,
less_than_wf,
list_n_properties,
iff_weakening_equal,
exp-positive-stronger,
le_wf,
int_seg_wf,
unit_wf2,
imax-list-ub,
subtype_rel_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
list_n_wf,
exp_wf2,
length-map,
l_exists_map,
l_exists_iff,
l_member_wf,
btrue_wf,
zero-le-nat,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
enum-fin-seq-true,
squash_wf,
true_wf,
list_wf,
select_member,
lelt_wf,
length_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
intEquality,
lambdaEquality,
because_Cache,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
sqequalRule,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
imageMemberEquality,
baseClosed,
productElimination,
natural_numberEquality,
independent_pairFormation,
axiomEquality,
setElimination,
rename,
unionEquality,
unionElimination,
addEquality,
setEquality,
dependent_pairFormation,
approximateComputation,
int_eqEquality,
productEquality,
universeEquality,
instantiate
Latex:
\mforall{}[M:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} \mBbbB{}) {}\mrightarrow{} (\mBbbN{}?)]. \mforall{}[m:\mBbbN{}]. (enum-fin-seq-max2(M;m) \mmember{} \mBbbN{})
Date html generated:
2019_06_20-PM-02_57_01
Last ObjectModification:
2018_08_21-PM-01_57_12
Theory : continuity
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