Nuprl Lemma : es-fix_wf
∀[es:EO]. ∀[T:Type]. ∀[f:T ⟶ T]. ∀[e:T]. (f**(e) ∈ T) supposing ∀x:T. f x c≤ x supposing strong-subtype(T;E)
Proof
Definitions occuring in Statement :
es-fix: f**(e),
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],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-fix: f**(e),
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],
all: ∀x:A. B[x],
implies: P ⇒ Q
Latex:
\mforall{}[es:EO]. \mforall{}[T:Type].
\mforall{}[f:T {}\mrightarrow{} T]. \mforall{}[e:T]. (f**(e) \mmember{} T) supposing \mforall{}x:T. f x c\mleq{} x supposing strong-subtype(T;E)
Date html generated:
2016_05_16-AM-09_22_40
Last ObjectModification:
2015_12_28-PM-09_52_21
Theory : new!event-ordering
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