### Nuprl Lemma : bpa-equiv_weakening

`∀p:{2...}. ∀a,b:basic-padic(p).  ((a = b ∈ basic-padic(p)) `` bpa-equiv(p;b;a))`

Proof

Definitions occuring in Statement :  bpa-equiv: `bpa-equiv(p;x;y)` basic-padic: `basic-padic(p)` int_upper: `{i...}` all: `∀x:A. B[x]` implies: `P `` Q` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` equiv_rel: `EquivRel(T;x,y.E[x; y])` and: `P ∧ Q` refl: `Refl(T;x,y.E[x; y])` implies: `P `` Q` prop: `ℙ` int_upper: `{i...}` guard: `{T}` subtype_rel: `A ⊆r B` nat_plus: `ℕ+` so_lambda: `λ2x.t[x]` so_apply: `x[s]` uimplies: `b supposing a` le: `A ≤ B` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` top: `Top` less_than': `less_than'(a;b)` true: `True`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality productElimination setElimination rename hypothesis natural_numberEquality dependent_functionElimination hyp_replacement equalitySymmetry sqequalRule dependent_set_memberEquality independent_pairFormation applyLambdaEquality applyEquality because_Cache lambdaEquality intEquality independent_isectElimination setEquality unionElimination voidElimination independent_functionElimination isect_memberEquality voidEquality

Latex:
\mforall{}p:\{2...\}.  \mforall{}a,b:basic-padic(p).    ((a  =  b)  {}\mRightarrow{}  bpa-equiv(p;b;a))

Date html generated: 2018_05_21-PM-03_25_01
Last ObjectModification: 2018_05_19-AM-08_22_31

Theory : rings_1

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