Nuprl Lemma : bag-order_wf
∀T:Type. (bag-order(T) ∈ Type)
Proof
Definitions occuring in Statement : 
bag-order: bag-order(T)
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
bag-order: bag-order(T)
, 
uall: ∀[x:A]. B[x]
, 
and: P ∧ Q
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
gt: i > j
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Lemmas referenced : 
le_wf, 
linorder_wf, 
gt_wf, 
less_than_wf, 
equal_wf, 
equal-wf-T-base, 
iff_wf, 
all_wf, 
bag_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalRule, 
setEquality, 
functionEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
hypothesis, 
because_Cache, 
intEquality, 
productEquality, 
lambdaEquality, 
applyEquality, 
baseClosed, 
natural_numberEquality, 
universeEquality
Latex:
\mforall{}T:Type.  (bag-order(T)  \mmember{}  Type)
Date html generated:
2016_05_15-PM-03_11_23
Last ObjectModification:
2016_01_16-AM-08_37_23
Theory : bags
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