Nuprl Lemma : es-causle-retraction
∀es:EO. ∀[T:Type]. ∀f:T ─→ T. ((∀x:T. f x c≤ x) ⇒ retraction(T;f)) supposing strong-subtype(T;E)
Proof
Definitions occuring in Statement :
es-causle: e c≤ e',
es-E: E,
event_ordering: EO,
strong-subtype: strong-subtype(A;B),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
retraction: retraction(T;f)
Lemmas :
strong-subtype_witness,
es-E_wf,
all_wf,
es-causle_wf,
strong-subtype_wf,
event_ordering_wf,
es-causl-swellfnd,
subtype_rel_dep_function,
nat_wf,
subtype_rel_self,
or_wf,
equal_wf,
less_than_wf,
strong-subtype-implies
\mforall{}es:EO. \mforall{}[T:Type]. \mforall{}f:T {}\mrightarrow{} T. ((\mforall{}x:T. f x c\mleq{} x) {}\mRightarrow{} retraction(T;f)) supposing strong-subtype(T;E)
Date html generated:
2015_07_17-AM-08_38_38
Last ObjectModification:
2015_01_27-PM-02_42_57
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