### Nuprl Lemma : bpa-equiv-iff-norm2

`∀p:{2...}. ∀x,y:basic-padic(p).  (bpa-norm(p;x) = bpa-norm(p;y) ∈ padic(p) `⇐⇒` bpa-equiv(p;x;y))`

Proof

Definitions occuring in Statement :  padic: `padic(p)` 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]` iff: `P `⇐⇒` Q` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` member: `t ∈ T` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` prop: `ℙ` uall: `∀[x:A]. B[x]` int_upper: `{i...}` nat_plus: `ℕ+` le: `A ≤ B` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` rev_implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` subtype_rel: `A ⊆r B` top: `Top` less_than': `less_than'(a;b)` true: `True`
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation hypothesis sqequalHypSubstitution dependent_functionElimination thin hypothesisEquality productElimination independent_pairFormation isectElimination setElimination rename dependent_set_memberEquality because_Cache natural_numberEquality unionElimination voidElimination independent_functionElimination independent_isectElimination sqequalRule applyEquality lambdaEquality isect_memberEquality voidEquality intEquality addLevel impliesFunctionality equalityTransitivity equalitySymmetry

Latex:
\mforall{}p:\{2...\}.  \mforall{}x,y:basic-padic(p).    (bpa-norm(p;x)  =  bpa-norm(p;y)  \mLeftarrow{}{}\mRightarrow{}  bpa-equiv(p;x;y))

Date html generated: 2018_05_21-PM-03_26_21
Last ObjectModification: 2018_05_19-AM-08_23_26

Theory : rings_1

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