Nuprl Lemma : es-local-prior-state-induction
∀[Info,T:Type]. ∀[P:T ⟶ ℙ].
∀es:EO+(Info)
∀[A:Type]
∀X:EClass(A). ∀base:T. ∀f:T ⟶ A ⟶ T. ∀e:E.
(P[base] ⇒ (∀x:T. ∀e':E(X). ((e' <loc e) ⇒ P[x] ⇒ P[f x X(e')])) ⇒ P[prior-state(f;base;X;e)])
Proof
Definitions occuring in Statement :
es-local-prior-state: prior-state(f;base;X;e),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
es-E-interface: E(X),
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
es-local-prior-state: prior-state(f;base;X;e),
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
es-locl: (e <loc e'),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}].
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}X:EClass(A). \mforall{}base:T. \mforall{}f:T {}\mrightarrow{} A {}\mrightarrow{} T. \mforall{}e:E.
(P[base]
{}\mRightarrow{} (\mforall{}x:T. \mforall{}e':E(X). ((e' <loc e) {}\mRightarrow{} P[x] {}\mRightarrow{} P[f x X(e')]))
{}\mRightarrow{} P[prior-state(f;base;X;e)])
Date html generated:
2016_05_17-AM-07_09_24
Last ObjectModification:
2015_12_29-AM-00_10_38
Theory : event-ordering
Home
Index