Nuprl Lemma : resigned_wf
∀[Pos:Type]. ∀[Mv:Pos ⟶ Type]. ∀[sg:Spread(Pos;a.Mv[a])?]. (resigned(sg) ∈ ℙ)
Proof
Definitions occuring in Statement :
resigned: resigned(x),
Spread: Spread(Pos;a.Mv[a]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
resigned: resigned(x),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
assert_wf,
isr_wf,
Spread_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
isect_memberEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[Pos:Type]. \mforall{}[Mv:Pos {}\mrightarrow{} Type]. \mforall{}[sg:Spread(Pos;a.Mv[a])?]. (resigned(sg) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_56_42
Last ObjectModification:
2015_12_26-PM-05_48_13
Theory : spread
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