Nuprl Lemma : fpf-rename-dom2
∀[A,C:Type]. ∀[eqa:EqDecider(A)]. ∀[eqc:EqDecider(C)]. ∀[eqc':Top]. ∀[r:A ─→ C]. ∀[f:a:A fp-> Top]. ∀[a:A].
{↑r a ∈ dom(rename(r;f)) supposing ↑a ∈ dom(f)}
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert-deq-member,
map_wf,
assert_witness,
deq-member_wf,
assert_wf,
fpf-dom_wf,
fpf_wf,
top_wf,
deq_wf,
member_map,
l_member_wf
\mforall{}[A,C:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[eqc:EqDecider(C)]. \mforall{}[eqc':Top]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> Top].
\mforall{}[a:A].
\{\muparrow{}r a \mmember{} dom(rename(r;f)) supposing \muparrow{}a \mmember{} dom(f)\}
Date html generated:
2015_07_17-AM-11_10_45
Last ObjectModification:
2015_01_28-AM-07_44_30
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