Nuprl Lemma : lifting1-loc-lifting-like
∀[A,B:Type]. ∀[f:Id ⟶ A ⟶ B]. ∀[i:Id]. lifting-like(A;λa.lifting1-loc(f;i;a))
Proof
Definitions occuring in Statement :
lifting-like: lifting-like(A;f),
lifting1-loc: lifting1-loc(f;loc;b),
Id: Id,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
lifting1-loc: lifting1-loc(f;loc;b),
lifting-like: lifting-like(A;f),
bag-null: bag-null(bs),
null: null(as),
lifting-loc-gen-rev: lifting-loc-gen-rev(n;bags;loc;f),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
bfalse: ff,
bag-combine: ⋃x∈bs.f[x],
bag-union: bag-union(bbs),
concat: concat(ll),
reduce: reduce(f;k;as),
list_ind: list_ind,
bag-map: bag-map(f;bs),
map: map(f;as),
single-bag: {x},
cons: [a / b],
append: as @ bs,
btrue: tt,
empty-bag: {},
nil: [],
it: ⋅,
assert: ↑b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
true: True,
uiff: uiff(P;Q),
uimplies: b supposing a,
guard: {T}
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B]. \mforall{}[i:Id]. lifting-like(A;\mlambda{}a.lifting1-loc(f;i;a))
Date html generated:
2016_05_17-AM-11_12_01
Last ObjectModification:
2015_12_29-PM-05_14_10
Theory : process-model
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