Nuprl Lemma : concat-lifting-0_wf
∀[B:Type]. ∀[f:bag(B)]. (concat-lifting-0(f) ∈ bag(B))
Proof
Definitions occuring in Statement :
concat-lifting-0: concat-lifting-0(f),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
concat-lifting-0: concat-lifting-0(f),
select: L[n],
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
funtype: funtype(n;A;T),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
bag-union: bag-union(bbs),
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
btrue: tt,
single-bag: {x},
cons: [a / b],
append: as @ bs
Lemmas referenced :
bag_wf,
primrec0_lemma,
int_seg_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
le_wf,
false_wf,
concat-lifting_wf,
base_wf,
stuck-spread
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
independent_isectElimination,
lambdaFormation,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaEquality,
because_Cache,
setElimination,
rename,
productElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
computeAll,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[B:Type]. \mforall{}[f:bag(B)]. (concat-lifting-0(f) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-03_07_39
Last ObjectModification:
2016_01_16-AM-08_34_30
Theory : bags
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