Nuprl Lemma : kind-rename-inj
∀[ra,rt:Id ⟶ Id]. (Inj(Knd;Knd;λk.kind-rename(ra;rt;k))) supposing (Inj(Id;Id;ra) and Inj(Id;Id;rt))
Proof
Definitions occuring in Statement :
kind-rename: kind-rename(ra;rt;k),
Knd: Knd,
Id: Id,
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
kind-rename: kind-rename(ra;rt;k),
inject: Inj(A;B;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
Knd: Knd,
rcv: rcv(l,tg),
locl: locl(a),
kindcase: kindcase(k;a.f[a];l,t.g[l; t]),
tagof: tag(k),
lnk: lnk(k),
actof: act(k),
islocal: islocal(k),
isl: isl(x),
outr: outr(x),
outl: outl(x),
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
pi1: fst(t),
pi2: snd(t),
bfalse: ff,
guard: {T},
and: P ∧ Q,
squash: ↓T,
true: True,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[ra,rt:Id {}\mrightarrow{} Id].
(Inj(Knd;Knd;\mlambda{}k.kind-rename(ra;rt;k))) supposing (Inj(Id;Id;ra) and Inj(Id;Id;rt))
Date html generated:
2016_05_16-AM-10_55_42
Last ObjectModification:
2016_01_17-PM-03_47_46
Theory : event-ordering
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