Nuprl Lemma : null-map
∀[f,L:Top]. (null(map(f;L)) ~ null(L))
Proof
Definitions occuring in Statement :
null: null(as),
map: map(f;as),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
null: null(as),
map: map(f;as),
list_ind: list_ind,
has-value: (a)↓,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
cons: [a / b],
bfalse: ff,
top: Top,
nil: [],
it: ⋅,
btrue: tt
Lemmas referenced :
bottom-sqle,
strictness-ispair,
has-value-implies-dec-isaxiom-2,
top_wf,
is-exception_wf,
has-value_wf_base,
has-value-implies-dec-ispair-2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalSqle,
sqleRule,
thin,
divergentSqle,
callbyvalueIspair,
sqequalHypSubstitution,
hypothesis,
callbyvalueCallbyvalue,
callbyvalueReduce,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
unionElimination,
sqleReflexivity,
isectElimination,
baseClosed,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
baseApply,
closedConclusion,
ispairExceptionCases,
axiomSqleEquality,
callbyvalueExceptionCases,
exceptionSqequal,
sqequalAxiom
Latex:
\mforall{}[f,L:Top]. (null(map(f;L)) \msim{} null(L))
Date html generated:
2016_05_14-AM-06_30_48
Last ObjectModification:
2016_01_14-PM-08_26_06
Theory : list_0
Home
Index