Nuprl Lemma : on-loc-class-program_wf
∀[Info,B:Type]. ∀[X:Id ⟶ EClass(B)]. ∀[pr:∀i:Id. LocalClass(X i)].
on-loc-class-program(pr) ∈ LocalClass(on-loc-class(X)) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
on-loc-class-program: on-loc-class-program(pr),
on-loc-class: on-loc-class(X),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
valueall-type: valueall-type(T),
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,
on-loc-class-program: on-loc-class-program(pr),
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
squash: ↓T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
class-ap: X(e),
on-loc-class: on-loc-class(X),
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:Id {}\mrightarrow{} EClass(B)]. \mforall{}[pr:\mforall{}i:Id. LocalClass(X i)].
on-loc-class-program(pr) \mmember{} LocalClass(on-loc-class(X)) supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_09_10
Last ObjectModification:
2016_01_17-PM-09_12_16
Theory : local!classes
Home
Index