Nuprl Lemma : insert-ordered-message_wf
∀[M:Type]. ∀[n:ℕ]. ∀[L:{L:({n + 1...} × M) List| sorted-by(λx,y. fst(x) < fst(y);L)} ]. ∀[x:{n + 1...} × M].
(insert-ordered-message(L;x) ∈ {L:({n + 1...} × M) List| sorted-by(λx,y. fst(x) < fst(y);L)} )
Proof
Definitions occuring in Statement :
insert-ordered-message: insert-ordered-message(L;x),
sorted-by: sorted-by(R;L),
list: T List,
int_upper: {i...},
nat: ℕ,
less_than: a < b,
uall: ∀[x:A]. B[x],
pi1: fst(t),
member: t ∈ T,
set: {x:A| B[x]} ,
lambda: λx.A[x],
product: x:A × B[x],
add: n + m,
natural_number: $n,
universe: Type
Lemmas :
sorted-by_wf,
l_member_wf,
less_than_wf,
int_upper_wf,
set_wf,
list_wf,
nat_wf,
insert-combine-sorted-by,
int-minus-comparison-inc_wf,
top_wf,
comparison_wf,
equal-wf-T-base,
subtract_wf,
select_wf,
length_wf,
int_seg_wf,
insert-combine_wf
Latex:
\mforall{}[M:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[L:\{L:(\{n + 1...\} \mtimes{} M) List| sorted-by(\mlambda{}x,y. fst(x) < fst(y);L)\} ].
\mforall{}[x:\{n + 1...\} \mtimes{} M].
(insert-ordered-message(L;x) \mmember{} \{L:(\{n + 1...\} \mtimes{} M) List| sorted-by(\mlambda{}x,y. fst(x) < fst(y);L)\} )
Date html generated:
2015_07_23-PM-00_27_43
Last ObjectModification:
2015_01_29-AM-01_29_30
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