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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