Nuprl Lemma : concat_iseg
∀[T:Type]. ∀ll1,ll2:T List List.  (ll1 ≤ ll2 
⇒ concat(ll1) ≤ concat(ll2))
Proof
Definitions occuring in Statement : 
iseg: l1 ≤ l2
, 
concat: concat(ll)
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
universe: Type
Definitions unfolded in proof : 
iseg: l1 ≤ l2
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
exists: ∃x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
top: Top
Lemmas referenced : 
exists_wf, 
list_wf, 
equal_wf, 
concat_wf, 
append_wf, 
concat_append
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
cut, 
hypothesis, 
hyp_replacement, 
equalitySymmetry, 
Error :applyLambdaEquality, 
introduction, 
extract_by_obid, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
lambdaEquality, 
universeEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
dependent_pairFormation, 
because_Cache
Latex:
\mforall{}[T:Type].  \mforall{}ll1,ll2:T  List  List.    (ll1  \mleq{}  ll2  {}\mRightarrow{}  concat(ll1)  \mleq{}  concat(ll2))
Date html generated:
2016_10_21-AM-10_35_04
Last ObjectModification:
2016_07_12-AM-05_46_12
Theory : list_1
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