Nuprl Lemma : map-conversion-test
∀[T:Type]. ∀[L:T List List]. (map(λX.(X @ []);L) ~ map(λX.X;L)) supposing T ⊆r Base
Proof
Definitions occuring in Statement : 
map: map(f;as)
, 
append: as @ bs
, 
nil: []
, 
list: T List
, 
uimplies: b supposing a
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
lambda: λx.A[x]
, 
base: Base
, 
universe: Type
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
top: Top
, 
prop: ℙ
Lemmas referenced : 
l_member_wf, 
top_wf, 
subtype_rel_list, 
append-nil, 
list_subtype_base, 
map_functionality_wrt_sq, 
base_wf, 
subtype_rel_wf, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalAxiom, 
hypothesis, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
sqequalRule, 
isect_memberEquality, 
because_Cache, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
independent_isectElimination, 
baseClosed, 
lambdaFormation, 
applyEquality, 
lambdaEquality, 
voidElimination, 
voidEquality
Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List  List].  (map(\mlambda{}X.(X  @  []);L)  \msim{}  map(\mlambda{}X.X;L))  supposing  T  \msubseteq{}r  Base
Date html generated:
2016_05_14-PM-01_57_39
Last ObjectModification:
2016_01_15-AM-08_11_37
Theory : list_1
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