### 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` implies: `P `` Q` all: `∀x:A. B[x]` top: `Top` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` prop: `ℙ` false: `False` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` not: `¬A` guard: `{T}` ge: `i ≥ j `
Lemmas referenced :  list_induction equal_wf nat_wf length_wf_nat map_wf list_wf map_nil_lemma length_of_nil_lemma decidable__equal_int satisfiable-full-omega-tt intformnot_wf intformeq_wf itermConstant_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_constant_lemma int_formula_prop_wf false_wf le_wf map_cons_lemma length_of_cons_lemma nat_properties length_wf intformand_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_term_value_add_lemma int_term_value_var_lemma add_nat_wf decidable__le intformle_wf int_formula_prop_le_lemma
Rules used in proof :  cut thin introduction extract_by_obid sqequalHypSubstitution sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isectElimination hypothesisEquality sqequalRule lambdaEquality hypothesis cumulativity functionExtensionality applyEquality independent_functionElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality natural_numberEquality because_Cache unionElimination independent_isectElimination dependent_pairFormation intEquality computeAll dependent_set_memberEquality equalityTransitivity equalitySymmetry independent_pairFormation lambdaFormation rename applyLambdaEquality setElimination addEquality int_eqEquality functionEquality universeEquality isect_memberFormation axiomEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B].  \mforall{}[as:A  List].    (||map(f;as)||  =  ||as||)

Date html generated: 2017_04_17-AM-08_44_32
Last ObjectModification: 2017_02_27-PM-05_02_02

Theory : list_1

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