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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
insert-ordered-message: insert-ordered-message(L;x),
all: ∀x:A. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
prop: ℙ,
pi1: fst(t),
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
implies: P ⇒ Q,
int-minus-comparison-inc: int-minus-comparison-inc(f),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
false: False,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
sorted-by: sorted-by(R;L),
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k
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:
2016_05_17-PM-00_56_34
Last ObjectModification:
2016_01_18-AM-07_40_17
Theory : event-logic-applications
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