Nuprl Lemma : concat-lifting1_wf
∀[A,B:Type]. ∀[f:A ⟶ bag(B)]. ∀[b:bag(A)]. (concat-lifting1(f;b) ∈ bag(B))
Proof
Definitions occuring in Statement :
concat-lifting1: concat-lifting1(f;bag),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
concat-lifting1: concat-lifting1(f;bag),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
funtype: funtype(n;A;T),
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
concat-lifting_wf,
false_wf,
le_wf,
int_seg_wf,
primrec1_lemma,
subtype_rel_self,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
lambdaEquality,
applyEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
axiomEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[b:bag(A)]. (concat-lifting1(f;b) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-03_07_14
Last ObjectModification:
2015_12_27-AM-09_26_49
Theory : bags
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