Nuprl Lemma : State-loc-comb-non-empty-iff

`∀[Info,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].`
`  ∀X:EClass(A). ∀es:EO+(Info). ∀e:E.  (¬↑bag-null(init loc(e)) `⇐⇒` ↓∃v:B. v ∈ State-loc-comb(init;f;X)(e))`

Proof

Definitions occuring in Statement :  State-loc-comb: `State-loc-comb(init;f;X)` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-loc: `loc(e)` es-E: `E` Id: `Id` assert: `↑b` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` exists: `∃x:A. B[x]` iff: `P `⇐⇒` Q` not: `¬A` squash: `↓T` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` bag-null: `bag-null(bs)` bag: `bag(T)`
Lemmas :  State-loc-comb-non-empty not_wf assert_wf bag-null_wf es-loc_wf State-loc-comb-classrel-non-loc classrel_wf State-comb_wf State-comb-exists-iff null-bag-size neg_assert_of_eq_int bag-size_wf nat_wf squash_wf exists_wf State-loc-comb_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf Id_wf bag_wf

Latex:
\mforall{}[Info,B,A:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  B].  \mforall{}[init:Id  {}\mrightarrow{}  bag(B)].
\mforall{}X:EClass(A).  \mforall{}es:EO+(Info).  \mforall{}e:E.
(\mneg{}\muparrow{}bag-null(init  loc(e))  \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}\mexists{}v:B.  v  \mmember{}  State-loc-comb(init;f;X)(e))

Date html generated: 2015_07_22-PM-00_23_47
Last ObjectModification: 2015_01_28-AM-10_11_09

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