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

Proof

Definitions occuring in Statement :  padic: `padic(p)` bpa-norm: `bpa-norm(p;x)` basic-padic: `basic-padic(p)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` basic-padic: `basic-padic(p)` nat_plus: `ℕ+` padic: `padic(p)` all: `∀x:A. B[x]` implies: `P `` Q` nat: `ℕ` 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 ` bfalse: `ff` exists: `∃x:A. B[x]` prop: `ℙ` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` false: `False` le: `A ≤ B` less_than': `less_than'(a;b)` not: `¬A` ge: `i ≥ j ` int_upper: `{i...}` bpa-norm: `bpa-norm(p;x)` so_lambda: `λ2x.t[x]` so_apply: `x[s]` pi2: `snd(t)` pi1: `fst(t)` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` p-adics: `p-adics(p)` decidable: `Dec(P)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtype_rel: `A ⊆r B` true: `True` int_seg: `{i..j-}` nequal: `a ≠ b ∈ T ` lelt: `i ≤ j < k` p-units: `p-units(p)` less_than: `a < b` squash: `↓T`
Lemmas referenced :  basic-padic_wf nat_plus_wf bpa-norm_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int upper_subtype_nat false_wf nat_properties nequal-le-implies zero-add le_wf ifthenelse_wf p-adics_wf p-units_wf pi2_wf nat_wf pi1_wf int_upper_properties nat_plus_properties full-omega-unsat intformand_wf intformeq_wf itermConstant_wf itermVar_wf intformle_wf int_formula_prop_and_lemma int_formula_prop_eq_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_formula_prop_wf decidable__lt not-lt-2 add_functionality_wrt_le add-commutes le-add-cancel less_than_wf int_seg_wf exp_wf2 p-unitize_wf p-mul_wf p-int_wf subtract_wf int_seg_properties decidable__le intformnot_wf itermSubtract_wf intformless_wf itermAdd_wf int_formula_prop_not_lemma int_term_value_subtract_lemma int_formula_prop_less_lemma int_term_value_add_lemma equal-wf-T-base not_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut sqequalHypSubstitution productElimination thin rename hypothesis introduction extract_by_obid isectElimination setElimination hypothesisEquality dependent_functionElimination sqequalRule independent_pairEquality lambdaFormation dependent_pairEquality natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry independent_isectElimination because_Cache dependent_pairFormation promote_hyp instantiate independent_functionElimination voidElimination hypothesis_subsumption independent_pairFormation dependent_set_memberEquality universeEquality applyLambdaEquality lambdaEquality approximateComputation int_eqEquality intEquality isect_memberEquality voidEquality cumulativity applyEquality productEquality addEquality setEquality imageMemberEquality baseClosed

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