Nuprl Lemma : msg-body-cmp_wf
∀[f:Name ─→ Type]. ∀[hdrs:Name List]. ∀[mcmp:hdr:Name ─→ comparison(f hdr)].
∀a:{x:Message(f)| (msg-header(x) ∈ hdrs)}
(msg-body-cmp(mcmp) ∈ comparison({b:{m:Message(f)| (msg-header(m) ∈ hdrs)} |
(list-index-cmp(NameDeq;hdrs;λm.msg-header(m)) a b) = 0 ∈ ℤ} ))
Proof
Definitions occuring in Statement :
msg-body-cmp: msg-body-cmp(mcmp),
msg-header: msg-header(m),
Message: Message(f),
name-deq: NameDeq,
name: Name,
list-index-cmp: list-index-cmp(eq;L;f),
comparison: comparison(T),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Lemmas :
set_wf,
Message_wf,
l_member_wf,
msg-header_wf,
comparison_wf,
list_wf,
name_wf,
compare-fun_wf,
msg-body_wf2,
subtype_rel-equal,
msg-type_wf,
iff_weakening_equal,
subtype_base_sq,
list_subtype_base,
atom_subtype_base,
all_wf,
equal_wf,
equal-wf-T-base,
le_wf,
member_wf,
subtype_rel_comparison,
list-index-cmp_wf,
name-deq_wf,
list-index-cmp-zero
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[hdrs:Name List]. \mforall{}[mcmp:hdr:Name {}\mrightarrow{} comparison(f hdr)].
\mforall{}a:\{x:Message(f)| (msg-header(x) \mmember{} hdrs)\}
(msg-body-cmp(mcmp) \mmember{} comparison(\{b:\{m:Message(f)| (msg-header(m) \mmember{} hdrs)\} |
(list-index-cmp(NameDeq;hdrs;\mlambda{}m.msg-header(m)) a b) = 0\} ))
Date html generated:
2015_07_22-PM-00_01_06
Last ObjectModification:
2015_02_04-PM-05_08_13
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