### 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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