### Nuprl Lemma : no_repeats_map

`∀[T:Type]. ∀[L:T List].  ∀[A:Type]. ∀[f:{x:T| (x ∈ L)}  ⟶ A].  no_repeats(A;map(f;L)) supposing Inj({x:T| (x ∈ L)} ;A;f\000C) supposing no_repeats(T;L)`

Proof

Definitions occuring in Statement :  no_repeats: `no_repeats(T;l)` l_member: `(x ∈ l)` map: `map(f;as)` list: `T List` inject: `Inj(A;B;f)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` set: `{x:A| B[x]} ` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  mapl: `mapl(f;l)` uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]` all: `∀x:A. B[x]` top: `Top` subtype_rel: `A ⊆r B` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` guard: `{T}` or: `P ∨ Q` uiff: `uiff(P;Q)` cand: `A c∧ B` inject: `Inj(A;B;f)` squash: `↓T` not: `¬A` exists: `∃x:A. B[x]` false: `False`
Lemmas referenced :  list_induction no_repeats_wf all_wf l_member_wf inject_wf mapl_wf list_wf map_nil_lemma no_repeats_nil nil_wf map_cons_lemma no_repeats_cons subtype_rel_dep_function cons_wf subtype_rel_sets cons_member equal_wf set_wf no_repeats_witness member_wf member-mapl and_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut thin extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality lambdaEquality functionEquality cumulativity hypothesis setEquality functionExtensionality applyEquality independent_functionElimination lambdaFormation dependent_functionElimination isect_memberEquality voidElimination voidEquality rename independent_isectElimination because_Cache setElimination productElimination inrFormation inlFormation dependent_set_memberEquality independent_pairFormation equalityTransitivity equalitySymmetry universeEquality hyp_replacement Error :applyLambdaEquality,  imageMemberEquality baseClosed imageElimination

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].
\mforall{}[A:Type].  \mforall{}[f:\{x:T|  (x  \mmember{}  L)\}    {}\mrightarrow{}  A].    no\_repeats(A;map(f;L))  supposing  Inj(\{x:T|  (x  \mmember{}  L)\}  ;A;f)  s\000Cupposing  no\_repeats(T;L)

Date html generated: 2016_10_21-AM-10_30_08
Last ObjectModification: 2016_07_12-AM-05_43_24

Theory : list_1

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