Nuprl Lemma : fpf-rename-cap3
∀[A,C,B:Type]. ∀[eqa:EqDecider(A)]. ∀[eqc,eqc':EqDecider(C)]. ∀[r:A ⟶ C]. ∀[f:a:A fp-> B]. ∀[a:A]. ∀[z:B]. ∀[c:C].
(rename(r;f)(c)?z = f(a)?z ∈ B) supposing ((c = (r a) ∈ C) and 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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q
Latex:
\mforall{}[A,C,B:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[eqc,eqc':EqDecider(C)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> B]. \mforall{}[a:A].
\mforall{}[z:B]. \mforall{}[c:C].
(rename(r;f)(c)?z = f(a)?z) supposing ((c = (r a)) and Inj(A;C;r))
Date html generated:
2016_05_16-AM-11_26_26
Last ObjectModification:
2015_12_29-AM-09_23_03
Theory : event-ordering
Home
Index