Nuprl Lemma : assert-cs-is-decided

∀[V:Type]. ∀x:consensus-state2(V). (↑cs-is-decided(x) ⇐⇒ ∃v:V. (x = Decided[v] ∈ consensus-state2(V)))


Proof




Definitions occuring in Statement :  cs-is-decided: cs-is-decided(x),  consensus-state2: consensus-state2(T),  cs-decided: Decided[v],  assert: ↑b,  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  exists: ∃x:A. B[x],  iff: P ⇐⇒ Q,  universe: Type,  equal: s = t ∈ T
Definitions unfolded in proof :  uall: ∀[x:A]. B[x],  all: ∀x:A. B[x],  consensus-state2: consensus-state2(T),  cs-decided: Decided[v],  cs-is-decided: cs-is-decided(x),  isl: isl(x),  assert: ↑b,  ifthenelse: if b then t else f fi ,  btrue: tt,  iff: P ⇐⇒ Q,  and: P ∧ Q,  implies: P ⇒ Q,  exists: ∃x:A. B[x],  member: t ∈ T,  prop: ℙ,  rev_implies: P ⇐ Q,  true: True,  so_lambda: λ2x.t[x],  so_apply: x[s],  bfalse: ff,  false: False,  not: ¬A

Latex:
\mforall{}[V:Type].  \mforall{}x:consensus-state2(V).  (\muparrow{}cs-is-decided(x)  \mLeftarrow{}{}\mRightarrow{}  \mexists{}v:V.  (x  =  Decided[v]))



Date html generated: 2016_05_16-AM-11_46_46
Last ObjectModification: 2015_12_29-PM-01_15_05

Theory : event-ordering


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