Nuprl Lemma : map_length_nat
∀[A,B:Type]. ∀[f:A ⟶ B]. ∀[as:A List]. (||map(f;as)|| = ||as|| ∈ ℕ)
Proof
Definitions occuring in Statement :
length: ||as||,
map: map(f;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
map-length,
length_wf_nat,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
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_35_09
Last ObjectModification:
2015_12_26-PM-00_35_06
Theory : list_0
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