Nuprl Lemma : map_length
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[as:A List]. (||map(f;as)|| = ||as|| ∈ ℤ)
Proof
Definitions occuring in Statement :
length: ||as||,
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
prop: ℙ
Lemmas referenced :
list_induction,
equal_wf,
length_wf,
map_wf,
list_wf,
map_nil_lemma,
length_of_nil_lemma,
map_cons_lemma,
length_of_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
intEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
lambdaFormation,
rename,
addEquality,
because_Cache,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[as:A List]. (||map(f;as)|| = ||as||)
Date html generated:
2016_05_14-AM-06_34_13
Last ObjectModification:
2015_12_26-PM-00_36_07
Theory : list_0
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