Nuprl Lemma : fpf-rename-cap
∀[A,C,B:Type]. ∀[eqa:EqDecider(A)]. ∀[eqc:EqDecider(C)]. ∀[r:A ⟶ C]. ∀[f:a:A fp-> B]. ∀[a:A]. ∀[z:B].
rename(r;f)(r a)?z = f(a)?z ∈ B supposing Inj(A;C;r)
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
fpf-cap: f(x)?z,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
guard: {T},
inject: Inj(A;B;f),
rev_implies: P ⇐ Q
Latex:
\mforall{}[A,C,B:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[eqc:EqDecider(C)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> B]. \mforall{}[a:A].
\mforall{}[z:B].
rename(r;f)(r a)?z = f(a)?z supposing Inj(A;C;r)
Date html generated:
2016_05_16-AM-11_26_11
Last ObjectModification:
2016_01_17-PM-03_48_26
Theory : event-ordering
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