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
Lemmas :
equal_wf,
fpf-cap_wf,
inject_wf,
fpf_wf,
deq_wf,
fpf-rename-cap2,
fpf-rename_wf
\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:
2015_07_17-AM-11_11_10
Last ObjectModification:
2015_01_28-AM-07_44_06
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