`∀[p:ℕ+]. ∀[x:padic(p)].  (bpa-norm(p;x) = x ∈ padic(p))`

Proof

Definitions occuring in Statement :  padic: `padic(p)` bpa-norm: `bpa-norm(p;x)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` padic: `padic(p)` bpa-norm: `bpa-norm(p;x)` member: `t ∈ T` nat: `ℕ` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` squash: `↓T` prop: `ℙ` nat_plus: `ℕ+` label: `...\$L... t` 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` subtype_rel: `A ⊆r B` eq_int: `(i =z j)` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` nequal: `a ≠ b ∈ T ` true: `True` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` le: `A ≤ B` less_than': `less_than'(a;b)` int_upper: `{i...}` p-units: `p-units(p)` int_seg: `{i..j-}` lelt: `i ≤ j < k` p-adics: `p-adics(p)` less_than: `a < b` p-unitize: `p-unitize(p;a;n)` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int equal_wf squash_wf true_wf nat_wf ifthenelse_wf p-adics_wf p-units_wf nat_properties nat_plus_properties decidable__equal_int full-omega-unsat intformand_wf intformnot_wf intformeq_wf itermVar_wf itermConstant_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_wf decidable__le intformle_wf int_formula_prop_le_lemma le_wf eqff_to_assert bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int subtype_rel_self iff_weakening_equal upper_subtype_nat false_wf nequal-le-implies zero-add p-adic-non-decreasing decidable__lt not-lt-2 add_functionality_wrt_le add-commutes le-add-cancel less_than_wf int_upper_properties intformless_wf itermAdd_wf int_formula_prop_less_lemma int_term_value_add_lemma lelt_wf le_weakening2 int_seg_wf exp_wf2 int_seg_properties padic_wf nat_plus_wf set_subtype_base int_subtype_base greatest-p-zero-property decidable__equal_nat greatest-p-zero_wf equal-wf-T-base subtract_wf itermSubtract_wf int_term_value_subtract_lemma not_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation sqequalHypSubstitution productElimination thin sqequalRule cut introduction extract_by_obid isectElimination setElimination rename hypothesisEquality hypothesis natural_numberEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry independent_isectElimination applyEquality lambdaEquality imageElimination universeEquality productEquality instantiate because_Cache dependent_pairEquality dependent_functionElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation dependent_set_memberEquality promote_hyp cumulativity imageMemberEquality baseClosed hypothesis_subsumption addEquality applyLambdaEquality functionExtensionality

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