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
Lemmas :
es-causle_weakening_eq,
event-ordering+_subtype,
es-causle_wf,
es-E-interface-property,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
subtype_rel_sets,
assert_wf,
in-eclass_wf,
es-interface-image_wf,
es-is-interface-image,
set_wf,
decidable__assert,
equal_wf,
interface_predicate_set_lemma,
es-E-interface_functionality,
es-E-interface_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-interface-image-val,
eclass-val_wf
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:
2015_07_21-PM-04_08_57
Last ObjectModification:
2015_01_27-PM-05_44_08
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