### Nuprl Lemma : bpa-norm-equiv

`∀p:{2...}. ∀x:basic-padic(p).  bpa-equiv(p;x;bpa-norm(p;x))`

Proof

Definitions occuring in Statement :  bpa-norm: `bpa-norm(p;x)` bpa-equiv: `bpa-equiv(p;x;y)` basic-padic: `basic-padic(p)` int_upper: `{i...}` all: `∀x:A. B[x]` natural_number: `\$n`
Definitions unfolded in proof :  all: `∀x:A. B[x]` basic-padic: `basic-padic(p)` bpa-norm: `bpa-norm(p;x)` bpa-equiv: `bpa-equiv(p;x;y)` member: `t ∈ T` uall: `∀[x:A]. B[x]` int_upper: `{i...}` nat: `ℕ` 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 ` top: `Top` 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 ` squash: `↓T` nat_plus: `ℕ+` decidable: `Dec(P)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` subtype_rel: `A ⊆r B` true: `True` p-adics: `p-adics(p)` int_seg: `{i..j-}` satisfiable_int_formula: `satisfiable_int_formula(fmla)` so_lambda: `λ2x.t[x]` subtract: `n - m` lelt: `i ≤ j < k` so_apply: `x[s]` nequal: `a ≠ b ∈ T ` p-units: `p-units(p)` crng: `CRng` rng: `Rng` p-adic-ring: `ℤ(p)` ring_p: `IsRing(T;plus;zero;neg;times;one)` rng_car: `|r|` pi1: `fst(t)` rng_plus: `+r` pi2: `snd(t)` rng_zero: `0` rng_minus: `-r` rng_times: `*` rng_one: `1` monoid_p: `IsMonoid(T;op;id)` group_p: `IsGroup(T;op;id;inv)` bilinear: `BiLinear(T;pl;tm)` ident: `Ident(T;op;id)` assoc: `Assoc(T;op)` inverse: `Inverse(T;op;id;inv)` infix_ap: `x f y` comm: `Comm(T;op)`
Lemmas referenced :  basic-padic_wf int_upper_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int exp0_lemma 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 int_subtype_base p-mul_wf squash_wf true_wf p-adics_wf nat_plus_wf decidable__lt not-lt-2 add_functionality_wrt_le add-commutes le-add-cancel less_than_wf p-int_wf int_seg_wf exp_wf2 p-adic-property nat_plus_properties int_upper_properties decidable__le full-omega-unsat intformnot_wf intformle_wf itermVar_wf itermAdd_wf itermConstant_wf int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_wf nat_plus_subtype_nat p-mul-1 p-shift_wf subtype_rel_self iff_weakening_equal p-shift-mul all_wf eqmod_wf less-iff-le condition-implies-le minus-add minus-one-mul minus-one-mul-top add-associates add-zero int_seg_properties intformand_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_less_lemma p-unitize_wf not-equal-2 p-units_wf int_seg_subtype_nat subtract_wf itermSubtract_wf int_term_value_subtract_lemma p-adic-ring_wf crng_properties rng_properties exp_add subtract-add-cancel decidable__equal_int intformeq_wf int_formula_prop_eq_lemma p-mul-int
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation sqequalHypSubstitution productElimination thin sqequalRule cut introduction extract_by_obid isectElimination setElimination rename hypothesisEquality hypothesis natural_numberEquality unionElimination equalityElimination equalityTransitivity equalitySymmetry independent_isectElimination dependent_functionElimination isect_memberEquality voidElimination voidEquality dependent_pairFormation promote_hyp instantiate cumulativity independent_functionElimination because_Cache hypothesis_subsumption independent_pairFormation dependent_set_memberEquality intEquality applyEquality lambdaEquality imageElimination imageMemberEquality baseClosed addEquality approximateComputation int_eqEquality universeEquality functionEquality minusEquality applyLambdaEquality productEquality setEquality equalityUniverse levelHypothesis

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