Nuprl Lemma : fRuleallE_wf
∀[hypnum:ℕ]. ∀[var:ℤ]. (allE on hypnum with var ∈ FOLRule())
Proof
Definitions occuring in Statement :
fRuleallE: allE on hypnum with var,
FOLRule: FOLRule(),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
FOLRule: FOLRule(),
fRuleallE: allE on hypnum with var,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
ifthenelse_wf,
eq_atom_wf,
unit_wf2,
bool_wf,
nat_wf,
istype-int,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalRule,
dependent_pairEquality_alt,
tokenEquality,
hypothesisEquality,
inhabitedIsType,
universeIsType,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
universeEquality,
intEquality,
productEquality,
voidEquality
Latex:
\mforall{}[hypnum:\mBbbN{}]. \mforall{}[var:\mBbbZ{}]. (allE on hypnum with var \mmember{} FOLRule())
Date html generated:
2020_05_20-AM-09_09_52
Last ObjectModification:
2020_01_24-PM-03_15_15
Theory : minimal-first-order-logic
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