Nuprl Lemma : es-interface-count-as-accum
∀[Info:Type]. ∀[X:EClass(Top)]. (#X = es-interface-accum(λn,x. (n + 1);0;X) ∈ EClass(ℕ))
Proof
Definitions occuring in Statement :
es-interface-accum: es-interface-accum(f;x;X),
es-interface-count: #X,
eclass: EClass(A[eo; e]),
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
add: n + m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
sv-class: Singlevalued(X),
es-interface-accum: es-interface-accum(f;x;X),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
subtype_rel: A ⊆r B,
es-interface-count: #X,
iff: P ⇐⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rev_implies: P ⇐ Q,
es-E-interface: E(X),
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info:Type]. \mforall{}[X:EClass(Top)]. (\#X = es-interface-accum(\mlambda{}n,x. (n + 1);0;X))
Date html generated:
2016_05_17-AM-07_21_10
Last ObjectModification:
2016_01_17-PM-03_02_46
Theory : event-ordering
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