Nuprl Lemma : FOLRule-ext
FOLRule() ≡ lbl:Atom × if lbl =a "andI" then Unit
if lbl =a "impI" then Unit
if lbl =a "allI" then ℤ
if lbl =a "existsI" then ℤ
if lbl =a "orI" then 𝔹
if lbl =a "hyp" then Unit
if lbl =a "andE" then ℕ
if lbl =a "orE" then ℕ
if lbl =a "impE" then ℕ
if lbl =a "allE" then hypnum:ℕ × ℤ
if lbl =a "existsE" then hypnum:ℕ × ℤ
if lbl =a "falseE" then ℕ
else Void
fi
Proof
Definitions occuring in Statement :
FOLRule: FOLRule(),
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bool: 𝔹,
ext-eq: A ≡ B,
unit: Unit,
product: x:A × B[x],
int: ℤ,
token: "$token",
atom: Atom,
void: Void
Definitions unfolded in proof :
FOLRule: FOLRule(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
ext-eq_weakening,
FOLRule_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
independent_isectElimination
Latex:
FOLRule() \mequiv{} lbl:Atom \mtimes{} if lbl =a "andI" then Unit
if lbl =a "impI" then Unit
if lbl =a "allI" then \mBbbZ{}
if lbl =a "existsI" then \mBbbZ{}
if lbl =a "orI" then \mBbbB{}
if lbl =a "hyp" then Unit
if lbl =a "andE" then \mBbbN{}
if lbl =a "orE" then \mBbbN{}
if lbl =a "impE" then \mBbbN{}
if lbl =a "allE" then hypnum:\mBbbN{} \mtimes{} \mBbbZ{}
if lbl =a "existsE" then hypnum:\mBbbN{} \mtimes{} \mBbbZ{}
if lbl =a "falseE" then \mBbbN{}
else Void
fi
Date html generated:
2016_05_15-PM-10_22_08
Last ObjectModification:
2015_12_27-PM-06_29_25
Theory : minimal-first-order-logic
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