Nuprl Lemma : Spread_wf
∀[Pos:Type]. ∀[Mv:Pos ⟶ Type]. (Spread(Pos;a.Mv[a]) ∈ Type)
Proof
Definitions occuring in Statement :
Spread: Spread(Pos;a.Mv[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Spread: Spread(Pos;a.Mv[a]),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
corec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
lambdaEquality,
productEquality,
hypothesisEquality,
functionEquality,
applyEquality,
universeEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[Pos:Type]. \mforall{}[Mv:Pos {}\mrightarrow{} Type]. (Spread(Pos;a.Mv[a]) \mmember{} Type)
Date html generated:
2016_05_14-PM-03_56_18
Last ObjectModification:
2015_12_26-PM-05_48_17
Theory : spread
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