Nuprl Lemma : eclass-state-classrel
∀[Info,A,B:Type]. ∀[init:Id ⟶ B]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
uiff(v ∈ eclass-state(init;f;X)(e);↓∃b:B
∃a:A
(a ∈ X(e)
∧ b ∈ Prior(eclass-state(init;f;X))?λl.{init l}(e)
∧ (v = (f loc(e) a b) ∈ B)))
Proof
Definitions occuring in Statement :
eclass-state: eclass-state(init;f;X),
primed-class-opt: Prior(X)?b,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x}
Definitions unfolded in proof :
eclass-state: eclass-state(init;f;X),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:B].
uiff(v \mmember{} eclass-state(init;f;X)(e);\mdownarrow{}\mexists{}b:B
\mexists{}a:A
(a \mmember{} X(e)
\mwedge{} b \mmember{} Prior(eclass-state(init;f;X))?\mlambda{}l.\{init l\}(e)
\mwedge{} (v = (f loc(e) a b))))
Date html generated:
2016_05_16-PM-11_47_38
Last ObjectModification:
2016_01_17-PM-07_04_28
Theory : event-ordering
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