Nuprl Lemma : vdf_wf
∀[A,B:Type]. ∀[C:A ⟶ B ⟶ Type]. ∀[n:ℤ]. (vdf(A;B;a,b.C[a;b];n) ∈ Type)
Proof
Definitions occuring in Statement :
vdf: vdf(A;B;a,b.C[a; b];n),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
and: P ∧ Q,
vdf: vdf(A;B;a,b.C[a; b];n),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla)
Lemmas referenced :
vdf-wf,
decidable__le,
istype-int,
istype-universe,
istype-le,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
list_wf,
equal-wf-base,
length_wf_nat,
set_subtype_base,
le_wf,
int_subtype_base,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
istype-less_than,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_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_formula_prop_less_lemma,
int_formula_prop_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
functionIsType,
universeIsType,
inhabitedIsType,
instantiate,
universeEquality,
dependent_set_memberEquality_alt,
productElimination,
closedConclusion,
because_Cache,
lambdaFormation_alt,
equalityElimination,
sqequalRule,
independent_isectElimination,
functionEquality,
setEquality,
productEquality,
applyEquality,
intEquality,
lambdaEquality_alt,
baseClosed,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation_alt,
equalityIstype,
promote_hyp,
cumulativity,
independent_functionElimination,
voidElimination,
approximateComputation,
int_eqEquality,
Error :memTop,
independent_pairFormation
Latex:
\mforall{}[A,B:Type]. \mforall{}[C:A {}\mrightarrow{} B {}\mrightarrow{} Type]. \mforall{}[n:\mBbbZ{}]. (vdf(A;B;a,b.C[a;b];n) \mmember{} Type)
Date html generated:
2020_05_19-PM-09_40_17
Last ObjectModification:
2020_03_05-AM-11_07_45
Theory : co-recursion-2
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