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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
msg-body-cmp: msg-body-cmp(mcmp),
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
msg-type: msg-type(msg;f),
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
compare-fun: compare-fun(cmp;f),
name: Name,
sq_type: SQType(T),
comparison: comparison(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
squash: ↓T,
uiff: uiff(P;Q)
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:
2016_05_17-AM-09_03_21
Last ObjectModification:
2016_01_17-PM-08_33_53
Theory : messages
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