Nuprl Lemma : eclass-state-program_wf
∀[Info,A,B:Type]. ∀[init:Id ⟶ B]. ∀[f:Id ⟶ A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[pr:LocalClass(X)].
eclass-state-program(init;f;pr) ∈ LocalClass(eclass-state(init;f;X)) supposing valueall-type(B) ∧ (↓B)
Proof
Definitions occuring in Statement :
eclass-state-program: eclass-state-program(init;f;pr),
eclass-state: eclass-state(init;f;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],
squash: ↓T,
and: P ∧ Q,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
squash: ↓T,
eclass-state-program: eclass-state-program(init;f;pr),
eclass-state: eclass-state(init;f;X),
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[pr:LocalClass(X)].
eclass-state-program(init;f;pr) \mmember{} LocalClass(eclass-state(init;f;X))
supposing valueall-type(B) \mwedge{} (\mdownarrow{}B)
Date html generated:
2016_05_17-AM-09_07_01
Last ObjectModification:
2016_01_17-PM-09_13_15
Theory : local!classes
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