### Nuprl Lemma : permutation-singleton

`∀[T:Type]. ∀[x:T]. ∀[ts:T List].  ts = [x] ∈ (T List) supposing permutation(T;[x];ts)`

Proof

Definitions occuring in Statement :  permutation: `permutation(T;L1;L2)` cons: `[a / b]` nil: `[]` list: `T List` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` all: `∀x:A. B[x]` or: `P ∨ Q` top: `Top` sq_type: `SQType(T)` implies: `P `` Q` guard: `{T}` true: `True` false: `False` cons: `[a / b]` squash: `↓T` ge: `i ≥ j ` le: `A ≤ B` and: `P ∧ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` prop: `ℙ` permutation: `permutation(T;L1;L2)` permute_list: `(L o f)` int_seg: `{i..j-}` so_lambda: `λ2x.t[x]` so_apply: `x[s]` lelt: `i ≤ j < k` decidable: `Dec(P)` less_than: `a < b` select: `L[n]`
Lemmas referenced :  top_wf length_cons_ge_one length_wf ge_wf squash_wf hd_wf reduce_hd_cons_lemma decidable__equal_int int_formula_prop_less_lemma intformless_wf decidable__lt int_formula_prop_not_lemma intformnot_wf lelt_wf int_seg_properties decidable__le set_subtype_base mklist-single list_wf permutation_wf int_formula_prop_wf int_term_value_add_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_and_lemma itermAdd_wf intformeq_wf itermVar_wf itermConstant_wf intformle_wf intformand_wf satisfiable-full-omega-tt non_neg_length product_subtype_list int_subtype_base subtype_base_sq length_of_nil_lemma length_of_cons_lemma list-cases nil_wf cons_wf permutation-length
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin because_Cache hypothesisEquality hypothesis independent_isectElimination dependent_functionElimination unionElimination sqequalRule isect_memberEquality voidElimination voidEquality instantiate cumulativity intEquality equalityTransitivity equalitySymmetry independent_functionElimination natural_numberEquality promote_hyp hypothesis_subsumption productElimination applyEquality lambdaEquality imageElimination imageMemberEquality baseClosed rename dependent_pairFormation int_eqEquality independent_pairFormation computeAll axiomEquality universeEquality setElimination setEquality dependent_set_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[x:T].  \mforall{}[ts:T  List].    ts  =  [x]  supposing  permutation(T;[x];ts)

Date html generated: 2016_05_14-PM-02_32_49
Last ObjectModification: 2016_01_15-AM-07_45_43

Theory : list_1

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