Nuprl Lemma : derived-seq_wf
∀[T:Type]. ∀[f:ℕ ⟶ T]. ∀[s:k:ℕ × (ℕk ⟶ ℕ)]. (derived-seq(f;s) ∈ ℕ ⟶ (k:ℕ × (ℕk ⟶ T)))
Proof
Definitions occuring in Statement :
derived-seq: derived-seq(f;s),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
derived-seq: derived-seq(f;s),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
nat_wf,
int_seg_wf,
add_nat_wf,
nat_properties,
int_seg_properties,
decidable__le,
add-is-int-iff,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_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_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
equal_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
productElimination,
thin,
lambdaEquality,
dependent_pairEquality,
hypothesisEquality,
applyEquality,
functionExtensionality,
extract_by_obid,
hypothesis,
dependent_set_memberEquality,
addEquality,
sqequalHypSubstitution,
setElimination,
rename,
isectElimination,
natural_numberEquality,
because_Cache,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
dependent_functionElimination,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
functionEquality,
cumulativity,
axiomEquality,
productEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T]. \mforall{}[s:k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} \mBbbN{})]. (derived-seq(f;s) \mmember{} \mBbbN{} {}\mrightarrow{} (k:\mBbbN{} \mtimes{} (\mBbbN{}k {}\mrightarrow{} T)))
Date html generated:
2018_05_21-PM-07_41_51
Last ObjectModification:
2017_07_26-PM-05_15_43
Theory : general
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