Nuprl Lemma : max-fst-val
∀[Info,A,T:Type].
∀[es:EO+(Info)]. ∀[X:EClass(T × A)]. ∀[e:E].
MaxFst(X)(e) ~ accum_list(p1,e.if fst(p1) <z fst(X(e)) then X(e) else p1 fi ;e.X(e);≤(X)(e))
supposing ↑e ∈b MaxFst(X)
supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
max-fst-class: MaxFst(X),
es-interface-predecessors: ≤(X)(e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
assert: ↑b,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
pi1: fst(t),
product: x:A × B[x],
int: ℤ,
universe: Type,
sqequal: s ~ t
Lemmas :
max-f-class-val,
assert_wf,
in-eclass_wf,
max-fst-class_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
eclass_wf,
subtype_rel_wf
Latex:
\mforall{}[Info,A,T:Type].
\mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T \mtimes{} A)]. \mforall{}[e:E].
MaxFst(X)(e) \msim{} accum\_list(p1,e.if fst(p1) <z fst(X(e)) then X(e) else p1 fi ;e.X(e);\mleq{}(X)(e))
supposing \muparrow{}e \mmember{}\msubb{} MaxFst(X)
supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2015_07_20-PM-03_51_17
Last ObjectModification:
2015_01_27-PM-10_08_00
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