Nuprl Lemma : WfdSpread_wf
∀[Pos:Type]. ∀[Mv:Pos ⟶ Type]. (WfdSpread(Pos;a.Mv[a]) ∈ Type)
Proof
Definitions occuring in Statement :
WfdSpread: WfdSpread(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,
WfdSpread: WfdSpread(Pos;a.Mv[a]),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Lemmas referenced :
Spread_wf,
all_wf,
nat_wf,
MoveChoice_wf,
squash_wf,
exists_wf,
resigned_wf,
subgame_wf,
subtype_rel_dep_function,
int_seg_wf,
int_seg_subtype_nat,
false_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
lambdaEquality,
applyEquality,
because_Cache,
hypothesis,
functionEquality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[Pos:Type]. \mforall{}[Mv:Pos {}\mrightarrow{} Type]. (WfdSpread(Pos;a.Mv[a]) \mmember{} Type)
Date html generated:
2016_05_14-PM-03_56_46
Last ObjectModification:
2015_12_26-PM-05_48_15
Theory : spread
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