Nuprl Lemma : subtype-set-hasloc
∀[i:Id]. ∀[d:{k:Knd| ↑hasloc(k;i)} List]. ({k:Knd| (k ∈ d)} ⊆r {k:{k:Knd| ↑hasloc(k;i)} | (k ∈ d)} )
Proof
Definitions occuring in Statement :
hasloc: hasloc(k;i),
Knd: Knd,
Id: Id,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
sq_type: SQType(T),
guard: {T},
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[i:Id]. \mforall{}[d:\{k:Knd| \muparrow{}hasloc(k;i)\} List]. (\{k:Knd| (k \mmember{} d)\} \msubseteq{}r \{k:\{k:Knd| \muparrow{}hasloc(k;i)\} | (k \mmember{} d)\000C\} )
Date html generated:
2016_05_16-AM-11_00_19
Last ObjectModification:
2016_01_17-PM-03_47_49
Theory : event-ordering
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