Nuprl Lemma : Q-Q-glues-to-self-image
∀[Info:Type]
∀es:EO+(Info)
∀[A,B:Type]. ∀Ia:EClass(A). ∀f:A ⟶ B. ∀[Q:E(Ia) ⟶ E(Ia) ⟶ ℙ]. λe.e glues Ia:Q ──λe.(f Ia(e))⟶ f'Ia:Q
Proof
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
es-E-interface: E(X),
es-interface-image: f'Ia,
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
top: Top,
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
implies: P ⇒ Q,
es-E-interface: E(X),
weak-antecedent-function: Q ←==f== P,
weak-antecedent-surjection: Q ←←= f== P,
es-interface-predicate: {I},
not: ¬A,
false: False,
or: P ∨ Q,
decidable: Dec(P),
exists: ∃x:A. B[x],
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
guard: {T},
sq_type: SQType(T),
inject: Inj(A;B;f)
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}f:A {}\mrightarrow{} B. \mforall{}[Q:E(Ia) {}\mrightarrow{} E(Ia) {}\mrightarrow{} \mBbbP{}]. \mlambda{}e.e glues Ia:Q {}{}\mlambda{}e.(f Ia(e)){}\mrightarrow{} f'Ia:Q
Date html generated:
2016_05_17-AM-07_50_26
Last ObjectModification:
2015_12_28-PM-11_29_52
Theory : event-ordering
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