Nuprl Lemma : fpf-rename-ap2

[A,C:Type]. ∀[B:A ─→ Type]. ∀[eqa:EqDecider(A)]. ∀[eqc,eqc':EqDecider(C)]. ∀[r:A ─→ C]. ∀[f:a:A fp-> B[a]]. ∀[a:A].
  (rename(r;f)(r a) f(a) ∈ B[a]) supposing ((↑a ∈ dom(f)) and Inj(A;C;r))


Definitions occuring in Statement :  fpf-rename: rename(r;f) fpf-ap: f(x) fpf-dom: x ∈ dom(f) fpf: a:A fp-> B[a] deq: EqDecider(T) inject: Inj(A;B;f) assert: b uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] apply: a function: x:A ─→ B[x] universe: Type equal: t ∈ T
Lemmas :  safe-assert-deq l_member_wf assert_wf assert-deq-member subtype_rel-equal iff_weakening_equal
\mforall{}[A,C:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[eqa:EqDecider(A)].  \mforall{}[eqc,eqc':EqDecider(C)].  \mforall{}[r:A  {}\mrightarrow{}  C].
\mforall{}[f:a:A  fp->  B[a]].  \mforall{}[a:A].
    (rename(r;f)(r  a)  =  f(a))  supposing  ((\muparrow{}a  \mmember{}  dom(f))  and  Inj(A;C;r))

Date html generated: 2015_07_17-AM-11_10_56
Last ObjectModification: 2015_02_04-PM-05_06_32

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