Step
*
1
of Lemma
interface-cmp_wf
.....wf.....
1. f : Name ─→ Type
2. locs : Id List
3. hdrs : Name List
4. mcmp : hdr:Name ─→ comparison(f hdr)
5. list-index-cmp(IdDeq;locs;λmi.mi.dst) ∈ comparison(Interface(to locs, with hdrs))
6. list-index-cmp(NameDeq;hdrs;λmi.msg-header(mi.msg)) ∈ comparison(Interface(to locs, with hdrs))
⊢ compare-fun(message-cmp(hdrs;mcmp);λmi.mi.msg) ∈ comparison(Interface(to locs, with hdrs))
BY
{ (Using [`B',⌈{m:Message(f)| (msg-header(m) ∈ hdrs)} ⌉] MemCD⋅ THEN Auto THEN D -1 THEN Auto) }
Latex:
Latex:
.....wf.....
1. f : Name {}\mrightarrow{} Type
2. locs : Id List
3. hdrs : Name List
4. mcmp : hdr:Name {}\mrightarrow{} comparison(f hdr)
5. list-index-cmp(IdDeq;locs;\mlambda{}mi.mi.dst) \mmember{} comparison(Interface(to locs, with hdrs))
6. list-index-cmp(NameDeq;hdrs;\mlambda{}mi.msg-header(mi.msg)) \mmember{} comparison(Interface(to locs, with hdrs))
\mvdash{} compare-fun(message-cmp(hdrs;mcmp);\mlambda{}mi.mi.msg) \mmember{} comparison(Interface(to locs, with hdrs))
By
Latex:
(Using [`B',\mkleeneopen{}\{m:Message(f)| (msg-header(m) \mmember{} hdrs)\} \mkleeneclose{}] MemCD\mcdot{} THEN Auto THEN D -1 THEN Auto)
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