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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