### Nuprl Lemma : pa-sep-irrefl

`∀[p:{2...}]. ∀x:basic-padic(p). (¬pa-sep(p;x;x))`

Proof

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

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