Nuprl Lemma : st-lookup_wf

[T:Id ⟶ Type]. ∀[tab:secret-table(T)]. ∀[x:Atom1].  (st-lookup(tab;x) ∈ ℕ Atom1 × data(T)?)


Proof




Definitions occuring in Statement :  st-lookup: st-lookup(tab;x) secret-table: secret-table(T) data: data(T) Id: Id nat: atom: Atom$n uall: [x:A]. B[x] unit: Unit member: t ∈ T function: x:A ⟶ B[x] product: x:A × B[x] union: left right universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T secret-table: secret-table(T) st-lookup: st-lookup(tab;x) spreadn: spread3 all: x:A. B[x] implies:  Q so_lambda: λ2x.t[x] nat: exposed-bfalse: exposed-bfalse bool: 𝔹 unit: Unit it: btrue: tt ifthenelse: if then else fi  uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a iff: ⇐⇒ Q prop: rev_implies:  Q bfalse: ff exists: x:A. B[x] or: P ∨ Q sq_type: SQType(T) guard: {T} bor: p ∨bq bnot: ¬bb assert: b false: False not: ¬A int_seg: {i..j-} lelt: i ≤ j < k ge: i ≥  decidable: Dec(P) satisfiable_int_formula: satisfiable_int_formula(fmla) top: Top le: A ≤ B so_apply: x[s] subtype_rel: A ⊆B true: True

Latex:
\mforall{}[T:Id  {}\mrightarrow{}  Type].  \mforall{}[tab:secret-table(T)].  \mforall{}[x:Atom1].    (st-lookup(tab;x)  \mmember{}  \mBbbN{}  +  Atom1  \mtimes{}  data(T)?)



Date html generated: 2016_05_16-AM-10_01_57
Last ObjectModification: 2016_01_17-PM-01_22_18

Theory : new!event-ordering


Home Index