### Nuprl Lemma : map_equal2

`∀[T,T':Type]. ∀[a:T List]. ∀[f,g:T ⟶ T'].`
`  map(f;a) = map(g;a) ∈ (T' List) supposing ∀x:T. ((x ∈ a) `` ((f x) = (g x) ∈ T'))`

Proof

Definitions occuring in Statement :  l_member: `(x ∈ l)` map: `map(f;as)` list: `T List` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` implies: `P `` Q` apply: `f a` function: `x:A ⟶ B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]` uimplies: `b supposing a` all: `∀x:A. B[x]` squash: `↓T` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` top: `Top` and: `P ∧ Q` int_seg: `{i..j-}` lelt: `i ≤ j < k` true: `True` subtype_rel: `A ⊆r B` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  all_wf l_member_wf equal_wf list_wf map_equal squash_wf true_wf select_wf nat_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf select_member lelt_wf length_wf subtype_rel_self iff_weakening_equal less_than_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality functionEquality hypothesis applyEquality because_Cache universeEquality isect_memberFormation isect_memberEquality axiomEquality equalityTransitivity equalitySymmetry independent_isectElimination lambdaFormation imageElimination dependent_functionElimination cumulativity setElimination rename natural_numberEquality unionElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality voidElimination voidEquality independent_pairFormation dependent_set_memberEquality functionExtensionality imageMemberEquality baseClosed instantiate productElimination

Latex:
\mforall{}[T,T':Type].  \mforall{}[a:T  List].  \mforall{}[f,g:T  {}\mrightarrow{}  T'].
map(f;a)  =  map(g;a)  supposing  \mforall{}x:T.  ((x  \mmember{}  a)  {}\mRightarrow{}  ((f  x)  =  (g  x)))

Date html generated: 2018_05_21-PM-06_20_19
Last ObjectModification: 2018_05_19-PM-05_32_25

Theory : list!

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