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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