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)
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
so_apply: x[s],
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
retraction: retraction(T;f),
nat: ℕ,
es-causle: e c≤ e',
or: P ∨ Q,
guard: {T},
label: ...$L... t,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Latex:
\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:
2016_05_16-AM-09_22_27
Last ObjectModification:
2015_12_28-PM-09_54_32
Theory : new!event-ordering
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