Nuprl Lemma : bind-class_local
∀[Info,A,B:Type].
∀[X:EClass(A)]. ∀[Y:A ─→ EClass(B)]. (LocalClass(X) ⇒ (∀a:A. LocalClass(Y[a])) ⇒ LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
bind-class: X >x> Y[x],
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
equal-wf-base,
base_wf,
bind-class-program_wf,
all_wf,
local-class_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
valueall-type_wf
Latex:
\mforall{}[Info,A,B:Type].
\mforall{}[X:EClass(A)]. \mforall{}[Y:A {}\mrightarrow{} EClass(B)].
(LocalClass(X) {}\mRightarrow{} (\mforall{}a:A. LocalClass(Y[a])) {}\mRightarrow{} LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Date html generated:
2015_07_22-PM-00_02_46
Last ObjectModification:
2015_01_28-AM-09_53_12
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