Step
*
1
1
1
2
1
of Lemma
bind-class-assoc
1. Info : Type
2. T : Type
3. S : Type
4. U : Type
5. X : es:EO+(Info) ─→ e:E ─→ bag(T)
6. Y : T ─→ es:EO+(Info) ─→ e:E ─→ bag(S)
7. Z : S ─→ es:EO+(Info) ─→ e:E ─→ bag(U)
8. es : EO+(Info)@i'
9. e : E@i
10. ≤loc(e) ∈ bag({e':E| e' ≤loc e } )
11. b : {e':E| e' ≤loc e } @i
⊢ ∪y∈∪a∈≤loc(b).∪x∈X es a.Y[x] es.a b.Z[y] es.b e = ∪y∈∪a∈≤loc(b).∪x∈X es a.Y[x] es.a b.Z[y] es.b e ∈ bag(U)
BY
{ (Assert ⌈≤loc(b) ∈ bag({e':E| e' ≤loc b } )⌉⋅ BY
(SubsumeC ⌈{e':E| e' ≤loc b } List⌉⋅
THEN Try ((BLemma `list-subtype-bag` THEN Auto))
THEN (BLemma `list_set_type` THEN Auto)
THEN BLemma `l_all_iff`
THEN Auto
THEN (BLemma `member-es-le-before` THEN Auto)⋅)) }
1
1. Info : Type
2. T : Type
3. S : Type
4. U : Type
5. X : es:EO+(Info) ─→ e:E ─→ bag(T)
6. Y : T ─→ es:EO+(Info) ─→ e:E ─→ bag(S)
7. Z : S ─→ es:EO+(Info) ─→ e:E ─→ bag(U)
8. es : EO+(Info)@i'
9. e : E@i
10. ≤loc(e) ∈ bag({e':E| e' ≤loc e } )
11. b : {e':E| e' ≤loc e } @i
12. ≤loc(b) ∈ bag({e':E| e' ≤loc b } )
⊢ ∪y∈∪a∈≤loc(b).∪x∈X es a.Y[x] es.a b.Z[y] es.b e = ∪y∈∪a∈≤loc(b).∪x∈X es a.Y[x] es.a b.Z[y] es.b e ∈ bag(U)
Latex:
1. Info : Type
2. T : Type
3. S : Type
4. U : Type
5. X : es:EO+(Info) {}\mrightarrow{} e:E {}\mrightarrow{} bag(T)
6. Y : T {}\mrightarrow{} es:EO+(Info) {}\mrightarrow{} e:E {}\mrightarrow{} bag(S)
7. Z : S {}\mrightarrow{} es:EO+(Info) {}\mrightarrow{} e:E {}\mrightarrow{} bag(U)
8. es : EO+(Info)@i'
9. e : E@i
10. \mleq{}loc(e) \mmember{} bag(\{e':E| e' \mleq{}loc e \} )
11. b : \{e':E| e' \mleq{}loc e \} @i
\mvdash{} \mcup{}y\mmember{}\mcup{}a\mmember{}\mleq{}loc(b).\mcup{}x\mmember{}X es a.Y[x] es.a b.Z[y] es.b e = \mcup{}y\mmember{}\mcup{}a\mmember{}\mleq{}loc(b).\mcup{}x\mmember{}X es a.Y[x] es.a b.Z[y] es.b e
By
(Assert \mkleeneopen{}\mleq{}loc(b) \mmember{} bag(\{e':E| e' \mleq{}loc b \} )\mkleeneclose{}\mcdot{} BY
(SubsumeC \mkleeneopen{}\{e':E| e' \mleq{}loc b \} List\mkleeneclose{}\mcdot{}
THEN Try ((BLemma `list-subtype-bag` THEN Auto))
THEN (BLemma `list\_set\_type` THEN Auto)
THEN BLemma `l\_all\_iff`
THEN Auto
THEN (BLemma `member-es-le-before` THEN Auto)\mcdot{}))
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