### Nuprl Lemma : nat-star-retract-id

`∀[s:ℕ*]. (nat-star-retract(s) = s ∈ ℕ*)`

Proof

Definitions occuring in Statement :  nat-star-retract: `nat-star-retract(s)` nat-star: `ℕ*` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat-star: `ℕ*` squash: `↓T` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]` all: `∀x:A. B[x]` nat-star-retract: `nat-star-retract(s)` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` iff: `P `⇐⇒` Q` guard: `{T}` ifthenelse: `if b then t else f fi ` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` bnot: `¬bb` assert: `↑b` rev_implies: `P `` Q` decidable: `Dec(P)` int_seg: `{i..j-}` ge: `i ≥ j ` lelt: `i ≤ j < k` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top`
Lemmas referenced :  nat-star-retract_wf nat-star_wf all_wf nat_wf less_than_wf equal_wf bl-exists_wf int_seg_wf upto_wf l_member_wf lt_int_wf int_seg_subtype_nat false_wf bool_wf eqtt_to_assert assert-bl-exists l_exists_functionality assert_wf iff_weakening_uiff subtype_rel_set assert_of_lt_int set_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot l_exists_wf l_exists_iff decidable__lt int_seg_properties nat_properties decidable__equal_int satisfiable-full-omega-tt intformand_wf intformeq_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf le_wf intformnot_wf itermConstant_wf intformle_wf int_formula_prop_not_lemma int_term_value_constant_lemma int_formula_prop_le_lemma not_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename hypothesisEquality hypothesis applyLambdaEquality sqequalRule imageMemberEquality baseClosed imageElimination dependent_set_memberEquality lambdaEquality functionEquality natural_numberEquality applyEquality functionExtensionality because_Cache intEquality lambdaFormation independent_isectElimination independent_pairFormation setEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry productElimination dependent_functionElimination independent_functionElimination promote_hyp dependent_pairFormation instantiate cumulativity voidElimination int_eqEquality isect_memberEquality voidEquality computeAll

Latex:
\mforall{}[s:\mBbbN{}*].  (nat-star-retract(s)  =  s)

Date html generated: 2017_04_17-AM-09_55_14
Last ObjectModification: 2017_02_27-PM-05_49_38

Theory : continuity

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