### Nuprl Lemma : p-mul_wf

`∀[p:ℕ+]. ∀[x,y:p-adics(p)].  (x * y ∈ p-adics(p))`

Proof

Definitions occuring in Statement :  p-mul: `x * y` p-adics: `p-adics(p)` nat_plus: `ℕ+` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` p-mul: `x * y` p-adics: `p-adics(p)` subtype_rel: `A ⊆r B` int_seg: `{i..j-}` nat_plus: `ℕ+` all: `∀x:A. B[x]` so_lambda: `λ2x.t[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` not: `¬A` rev_implies: `P `` Q` implies: `P `` Q` false: `False` prop: `ℙ` uiff: `uiff(P;Q)` uimplies: `b supposing a` subtract: `n - m` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True` nat: `ℕ` guard: `{T}` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` lelt: `i ≤ j < k` so_apply: `x[s]` int_upper: `{i...}`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution setElimination thin rename dependent_set_memberEquality lambdaEquality extract_by_obid isectElimination hypothesisEquality applyEquality hypothesis multiplyEquality natural_numberEquality because_Cache lambdaFormation addEquality dependent_functionElimination unionElimination independent_pairFormation voidElimination productElimination independent_functionElimination independent_isectElimination minusEquality approximateComputation dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidEquality equalityTransitivity equalitySymmetry applyLambdaEquality axiomEquality functionExtensionality

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