Nuprl Lemma : CV_wf
∀[A:Type]. ∀[F:t:ℕ ⟶ (ℕt ⟶ A) ⟶ A]. (CV(F) ∈ ℕ ⟶ A)
Proof
Definitions occuring in Statement :
CV: CV(F),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
all: ∀x:A. B[x],
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,
decidable: Dec(P),
or: P ∨ Q,
CV: CV(F),
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
int_seg_subtype,
subtype_rel_dep_function,
int_seg_properties,
false_wf,
int_seg_subtype_nat,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
lemma_by_obid,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
lambdaFormation,
intWeakElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
unionElimination,
applyEquality,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}[F:t:\mBbbN{} {}\mrightarrow{} (\mBbbN{}t {}\mrightarrow{} A) {}\mrightarrow{} A]. (CV(F) \mmember{} \mBbbN{} {}\mrightarrow{} A)
Date html generated:
2016_05_15-PM-04_32_33
Last ObjectModification:
2016_01_16-AM-11_17_04
Theory : general
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