Nuprl Lemma : fpf-rename-ap
∀[A,C:Type]. ∀[B:A ─→ Type]. ∀[eqa:EqDecider(A)]. ∀[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))
Proof
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: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = 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: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_50
Last ObjectModification:
2015_02_04-PM-05_06_24
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