Nuprl Lemma : simple-comb-2-classrel-weak

`∀[Info,A,B,C:Type]. ∀[f:A ─→ B ─→ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].`
`  (v ∈ lifting-2(f)|X, Y|(e) `⇐⇒` ↓∃a:A. ∃b:B. ((v = (f a b) ∈ C) ∧ b ∈ Y(e) ∧ a ∈ X(e)))`

Proof

Definitions occuring in Statement :  simple-comb-2: `F|X, Y|` classrel: `v ∈ X(e)` eclass: `EClass(A[eo; e])` event-ordering+: `EO+(Info)` es-E: `E` uall: `∀[x:A]. B[x]` exists: `∃x:A. B[x]` iff: `P `⇐⇒` Q` squash: `↓T` and: `P ∧ Q` apply: `f a` function: `x:A ─→ B[x]` universe: `Type` equal: `s = t ∈ T` lifting-2: `lifting-2(f)`
Lemmas :  simple-comb-2-classrel classrel_wf simple-comb-2_wf lifting-2_wf squash_wf exists_wf es-E_wf event-ordering+_subtype event-ordering+_wf eclass_wf

Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  C].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
\mforall{}[v:C].
(v  \mmember{}  lifting-2(f)|X,  Y|(e)  \mLeftarrow{}{}\mRightarrow{}  \mdownarrow{}\mexists{}a:A.  \mexists{}b:B.  ((v  =  (f  a  b))  \mwedge{}  b  \mmember{}  Y(e)  \mwedge{}  a  \mmember{}  X(e)))

Date html generated: 2015_07_22-PM-00_11_04
Last ObjectModification: 2015_01_28-AM-11_40_40

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