Nuprl Lemma : p-sep-irrefl
∀[p:ℕ+]. ∀[x:p-adics(p)]. (¬p-sep(x;x))
Proof
Definitions occuring in Statement :
p-sep: p-sep(x;y),
p-adics: p-adics(p),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
p-sep: p-sep(x;y),
exists: ∃x:A. B[x],
prop: ℙ,
nat_plus: ℕ+,
p-adics: p-adics(p),
subtype_rel: A ⊆r B,
int_seg: {i..j-}
Lemmas referenced :
p-sep_wf,
p-adics_wf,
nat_plus_wf,
int_seg_wf,
exp_wf2,
nat_plus_subtype_nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
productElimination,
independent_functionElimination,
voidElimination,
because_Cache,
hypothesis,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
setElimination,
rename,
isect_memberEquality,
applyEquality,
natural_numberEquality
Latex:
\mforall{}[p:\mBbbN{}\msupplus{}]. \mforall{}[x:p-adics(p)]. (\mneg{}p-sep(x;x))
Date html generated:
2018_05_21-PM-03_23_18
Last ObjectModification:
2018_05_19-AM-08_21_35
Theory : rings_1
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