Nuprl Lemma : map_swap
∀[A,B:Type]. ∀[f:B ⟶ A]. ∀[x:B List]. ∀[i,j:ℕ||x||]. (map(f;swap(x;i;j)) = swap(map(f;x);i;j) ∈ (A List))
Proof
Definitions occuring in Statement :
swap: swap(L;i;j),
length: ||as||,
map: map(f;as),
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
swap: swap(L;i;j)
Lemmas referenced :
map_permute_list,
flip_wf,
length_wf_nat,
int_seg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
natural_numberEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:B {}\mrightarrow{} A]. \mforall{}[x:B List]. \mforall{}[i,j:\mBbbN{}||x||]. (map(f;swap(x;i;j)) = swap(map(f;x);i;j))
Date html generated:
2016_05_15-PM-02_05_06
Last ObjectModification:
2015_12_27-AM-00_22_00
Theory : list!
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