Nuprl Lemma : State1-prior
∀[Info,A,B:Type]. ∀[init:Id ⟶ B]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E].
(Prior(State1(init;f;X))?λloc.{init loc}(e)
= if first(e) then {init loc(e)} else State1(init;f;X)(pred(e)) fi
∈ bag(B))
Proof
Definitions occuring in Statement :
State1: State1(init;tr;X),
primed-class-opt: Prior(X)?b,
class-ap: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
Id: Id,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
class-ap: X(e),
primed-class-opt: Prior(X)?b,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q,
sq_exists: ∃x:{A| B[x]},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
not: ¬A,
false: False,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-locl: (e <loc e'),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
classrel: v ∈ X(e),
cand: A c∧ B
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].
(Prior(State1(init;f;X))?\mlambda{}loc.\{init loc\}(e)
= if first(e) then \{init loc(e)\} else State1(init;f;X)(pred(e)) fi )
Date html generated:
2016_05_17-AM-10_04_28
Last ObjectModification:
2016_01_17-PM-11_04_32
Theory : classrel!lemmas
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