Nuprl Lemma : coded-seq_wf
∀x:ℕ. (coded-seq(x) ∈ k:ℕ × (ℕk ⟶ ℕ))
Proof
Definitions occuring in Statement :
coded-seq: coded-seq(x),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
coded-seq: coded-seq(x),
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
subtype_rel: A ⊆r B,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
eq_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
false_wf,
le_wf,
int_seg_subtype_nat,
int_seg_wf,
nat_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
coded-pair_wf,
subtract_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
itermAdd_wf,
int_term_value_add_lemma,
coded-seq1_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
because_Cache,
intEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
dependent_pairEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaEquality,
applyEquality,
functionEquality,
impliesFunctionality,
dependent_functionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
productEquality,
addEquality
Latex:
\mforall{}x:\mBbbN{}. (coded-seq(x) \mmember{} k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} \mBbbN{}))
Date html generated:
2019_06_20-PM-02_40_28
Last ObjectModification:
2019_06_12-PM-00_28_29
Theory : num_thy_1
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