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:  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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