Nuprl Lemma : fpf-restrict-compatible
∀[A:Type]. ∀[P:A ─→ 𝔹]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f,g:x:A fp-> B[x]].
fpf-restrict(f;P) || g supposing f || g
Proof
Definitions occuring in Statement :
fpf-restrict: fpf-restrict(f;P),
fpf-compatible: f || g,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type
Lemmas :
ap_fpf_restrict_lemma,
fpf-restrict-dom,
assert_wf,
fpf-dom_wf,
fpf-restrict_wf2,
top_wf,
subtype-fpf2,
subtype_top,
all_wf,
fpf-ap_wf,
fpf_wf,
deq_wf,
bool_wf
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f,g:x:A fp-> B[x]].
fpf-restrict(f;P) || g supposing f || g
Date html generated:
2015_07_17-AM-11_15_04
Last ObjectModification:
2015_01_28-AM-07_39_58
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