Nuprl Lemma : decidable__existse-before

es:EO. ∀e':E.  ∀[P:{e:E| loc(e) loc(e') ∈ Id}  ⟶ ℙ]. (∀e@loc(e').Dec(P[e])  Dec(∃e<e'.P[e]))


Proof




Definitions occuring in Statement :  existse-before: e<e'.P[e] alle-at: e@i.P[e] es-loc: loc(e) es-E: E event_ordering: EO Id: Id decidable: Dec(P) uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] implies:  Q set: {x:A| B[x]}  function: x:A ⟶ B[x] equal: t ∈ T
Definitions unfolded in proof :  all: x:A. B[x] member: t ∈ T subtype_rel: A ⊆B uall: [x:A]. B[x] prop: so_lambda: λ2x.t[x] implies:  Q so_apply: x[s] wellfounded: WellFnd{i}(A;x,y.R[x; y]) guard: {T} cand: c∧ B es-E: E es-base-E: es-base-E(es) uimplies: supposing a iff: ⇐⇒ Q and: P ∧ Q rev_implies:  Q or: P ∨ Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) assert: b ifthenelse: if then else fi  not: ¬A true: True false: False bfalse: ff exists: x:A. B[x] sq_type: SQType(T) bnot: ¬bb alle-at: e@i.P[e]

Latex:
\mforall{}es:EO.  \mforall{}e':E.    \mforall{}[P:\{e:E|  loc(e)  =  loc(e')\}    {}\mrightarrow{}  \mBbbP{}].  (\mforall{}e@loc(e').Dec(P[e])  {}\mRightarrow{}  Dec(\mexists{}e<e'.P[e]))



Date html generated: 2016_05_16-AM-09_41_25
Last ObjectModification: 2015_12_28-PM-09_43_31

Theory : new!event-ordering


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