Nuprl Lemma : local-class-equality
∀[Info,A:Type]. ∀[X:EClass(A)].
∀p,q:LocalClass(X).
p = q ∈ (Id ⟶ hdataflow(Info;A))
supposing ∀i:Id. ∀inputs:Info List. hdf-halted(p i*(inputs)) = hdf-halted(q i*(inputs))
Proof
Definitions occuring in Statement :
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
iterate-hdataflow: P*(inputs),
hdf-halted: hdf-halted(P),
hdataflow: hdataflow(A;B),
Id: Id,
list: T List,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
uiff: uiff(P;Q),
and: P ∧ Q,
cand: A c∧ B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
exists: ∃x:A. B[x],
Id: Id,
sq_type: SQType(T),
hdf-out: hdf-out(P;x),
top: Top,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
decidable: Dec(P),
or: P ∨ Q,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
listp: A List+,
es-le-before: ≤loc(e),
cons: [a / b],
nat: ℕ,
le: A ≤ B,
subtract: n - m
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)].
\mforall{}p,q:LocalClass(X).
p = q supposing \mforall{}i:Id. \mforall{}inputs:Info List. hdf-halted(p i*(inputs)) = hdf-halted(q i*(inputs))
Date html generated:
2016_05_17-AM-08_47_22
Last ObjectModification:
2016_01_17-PM-02_41_23
Theory : event-ordering
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