Nuprl Lemma : enum-fin-seq-true
∀m:ℕ. ((λx.tt) = enum-fin-seq(m)[0] ∈ (ℕ ⟶ 𝔹))
Proof
Definitions occuring in Statement :
enum-fin-seq: enum-fin-seq(m),
select: L[n],
nat: ℕ,
btrue: tt,
bool: 𝔹,
all: ∀x:A. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
enum-fin-seq: enum-fin-seq(m),
select: L[n],
cons: [a / b],
decidable: Dec(P),
or: P ∨ Q,
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,
squash: ↓T,
nequal: a ≠ b ∈ T ,
int_seg: {i..j-},
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
list_n: A List(n),
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
nat_plus: ℕ+,
less_than: a < b
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
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,
less_than_wf,
primrec0_lemma,
btrue_wf,
nat_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
primrec-unroll,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
squash_wf,
true_wf,
select_append_front,
map_wf,
primrec_wf,
list_wf,
le_wf,
cons_wf,
nil_wf,
append_wf,
bfalse_wf,
int_seg_wf,
iff_weakening_equal,
length-map,
enum-fin-seq_wf,
list_n_wf,
exp_wf2,
false_wf,
list_n_properties,
exp-positive-stronger,
lelt_wf,
length_wf,
select-map,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
because_Cache,
promote_hyp,
instantiate,
cumulativity,
applyEquality,
imageElimination,
universeEquality,
functionEquality,
functionExtensionality,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
int_eqReduceTrueSq,
int_eqReduceFalseSq
Latex:
\mforall{}m:\mBbbN{}. ((\mlambda{}x.tt) = enum-fin-seq(m)[0])
Date html generated:
2017_04_20-AM-07_22_41
Last ObjectModification:
2017_02_27-PM-05_59_09
Theory : continuity
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