Nuprl Lemma : strict-bag-function_wf
∀[L:Type List]. ∀[B:Type]. ∀[G:tuple-type(map(λT.bag(T);L)) ⟶ bag(B)]. ∀[S:ℕ||L|| List].
(strict-bag-function(G;L;B;S) ∈ ℙ)
Proof
Definitions occuring in Statement :
strict-bag-function: strict-bag-function(G;L;B;S),
bag: bag(T),
tuple-type: tuple-type(L),
length: ||as||,
map: map(f;as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strict-bag-function: strict-bag-function(G;L;B;S),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
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,
so_apply: x[s],
subtype_rel: A ⊆r B,
cand: A c∧ B
Lemmas referenced :
subtype_rel_self,
top_wf,
subtype_rel_list,
select-map,
map_length,
map-length,
int_seg_subtype_nat,
select-tuple_wf,
list_wf,
equal-wf-T-base,
empty-bag_wf,
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,
int_seg_properties,
select_wf,
equal_wf,
l_member_wf,
length_wf,
int_seg_wf,
l_all_wf,
bag_wf,
map_wf,
tuple-type_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
universeEquality,
because_Cache,
lambdaEquality,
cumulativity,
hypothesisEquality,
hypothesis,
functionEquality,
natural_numberEquality,
lambdaFormation,
setElimination,
rename,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
setEquality,
applyEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L:Type List]. \mforall{}[B:Type]. \mforall{}[G:tuple-type(map(\mlambda{}T.bag(T);L)) {}\mrightarrow{} bag(B)]. \mforall{}[S:\mBbbN{}||L|| List].
(strict-bag-function(G;L;B;S) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-02_58_46
Last ObjectModification:
2016_01_16-AM-08_39_33
Theory : bags
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