Nuprl Lemma : Spread-family_wf
∀[P,Pos:Type]. ∀[f:Pos ⟶ ℤ]. ∀[Mv:p:ℤ ⟶ P ⟶ P ⟶ Type]. (Spread-family(P;Pos;f;n,p,q.Mv[n;p;q]) ∈ P ⟶ Type)
Proof
Definitions occuring in Statement :
Spread-family: Spread-family(P;Pos;f;n,p,q.Mv[n; p; q]),
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Spread-family: Spread-family(P;Pos;f;n,p,q.Mv[n; p; q]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
corec-family_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
productEquality,
functionEquality,
applyEquality,
cumulativity,
universeEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P,Pos:Type]. \mforall{}[f:Pos {}\mrightarrow{} \mBbbZ{}]. \mforall{}[Mv:p:\mBbbZ{} {}\mrightarrow{} P {}\mrightarrow{} P {}\mrightarrow{} Type].
(Spread-family(P;Pos;f;n,p,q.Mv[n;p;q]) \mmember{} P {}\mrightarrow{} Type)
Date html generated:
2016_05_14-PM-03_57_15
Last ObjectModification:
2015_12_26-PM-05_48_12
Theory : spread
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