Nuprl Lemma : fpf-rename_wf
∀[A,C:Type]. ∀[B:A ─→ Type]. ∀[D:C ─→ Type]. ∀[eq:EqDecider(C)]. ∀[r:A ─→ C]. ∀[f:a:A fp-> B[a]].
rename(r;f) ∈ c:C fp-> D[c] supposing ∀a:A. (D[r a] = B[a] ∈ Type)
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
l_member_wf,
subtype_rel-equal,
iff_weakening_equal,
equal_wf,
hd-filter,
member_map,
safe-assert-deq,
assert_wf
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[D:C {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(C)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> B[a]].
rename(r;f) \mmember{} c:C fp-> D[c] supposing \mforall{}a:A. (D[r a] = B[a])
Date html generated:
2015_07_17-AM-11_10_38
Last ObjectModification:
2015_02_04-PM-05_15_05
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