Nuprl Lemma : sub-spread_wf
∀[Pos:Type]. ∀[Mv:Pos ⟶ Type]. ∀[s',s:Spread(Pos;a.Mv[a])].  (s' ≤ s ∈ ℙ)
Proof
Definitions occuring in Statement : 
sub-spread: s' ≤ s
, 
Spread: Spread(Pos;a.Mv[a])
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
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
, 
sub-spread: s' ≤ s
, 
so_lambda: λ2x.t[x]
, 
nat: ℕ
, 
so_apply: x[s]
Lemmas referenced : 
exists_wf, 
nat_wf, 
int_seg_wf, 
MoveChoice_wf, 
equal_wf, 
Spread_wf, 
unit_wf2, 
subgame_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
lambdaEquality, 
functionEquality, 
natural_numberEquality, 
setElimination, 
rename, 
hypothesisEquality, 
cumulativity, 
applyEquality, 
because_Cache, 
unionEquality, 
inlEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[Pos:Type].  \mforall{}[Mv:Pos  {}\mrightarrow{}  Type].  \mforall{}[s',s:Spread(Pos;a.Mv[a])].    (s'  \mleq{}  s  \mmember{}  \mBbbP{})
Date html generated:
2016_05_14-PM-03_56_28
Last ObjectModification:
2015_12_26-PM-05_48_13
Theory : spread
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