Nuprl Lemma : generic_wf
∀[T:Type]. ∀[S:(ℕ ⟶ T) ⟶ ℙ']. (Generic{f:ℕ⟶T|S[f]} ∈ ℙ')
Proof
Definitions occuring in Statement :
generic: Generic{f:ℕ⟶T|S[f]},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
generic: Generic{f:ℕ⟶T|S[f]},
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
implies: P ⇒ Q,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
less_than': less_than'(a;b)
Lemmas referenced :
false_wf,
int_seg_subtype_nat,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
int_seg_properties,
select_wf,
equal_wf,
length_wf,
int_seg_wf,
iseg_wf,
all_wf,
list_wf,
nat_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
productEquality,
because_Cache,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[S:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbP{}']. (Generic\{f:\mBbbN{}{}\mrightarrow{}T|S[f]\} \mmember{} \mBbbP{}')
Date html generated:
2016_05_15-PM-04_42_38
Last ObjectModification:
2016_01_16-AM-11_21_36
Theory : general
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