### Nuprl Lemma : for_wf

[A,B,C:Type]. ∀[f:B ⟶ C ⟶ C]. ∀[k:C]. ∀[as:A List]. ∀[g:A ⟶ B].  (For{A,f,k} x ∈ as. g[x] ∈ C)

Proof

Definitions occuring in Statement :  for: For{T,op,id} x ∈ as. f[x] list: List uall: [x:A]. B[x] so_apply: x[s] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T for: For{T,op,id} x ∈ as. f[x] tlambda: λx:T. b[x] so_apply: x[s]
Lemmas referenced :  reduce_wf map_wf list_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality applyEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry Error :functionIsType,  Error :universeIsType,  isect_memberEquality functionEquality because_Cache Error :inhabitedIsType,  universeEquality

Latex:
\mforall{}[A,B,C:Type].  \mforall{}[f:B  {}\mrightarrow{}  C  {}\mrightarrow{}  C].  \mforall{}[k:C].  \mforall{}[as:A  List].  \mforall{}[g:A  {}\mrightarrow{}  B].    (For\{A,f,k\}  x  \mmember{}  as.  g[x]  \mmember{}  C)

Date html generated: 2019_06_20-PM-00_39_11
Last ObjectModification: 2018_09_26-PM-02_05_45

Theory : list_0

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