### Nuprl Lemma : bpa-equiv_transitivity

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

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`
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` trans: `Trans(T;x,y.E[x; y])`
Lemmas referenced :  bpa-equiv-equiv int_upper_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality productElimination hypothesis natural_numberEquality

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

Date html generated: 2018_05_21-PM-03_24_53
Last ObjectModification: 2018_05_19-AM-08_22_20

Theory : rings_1

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