Nuprl Lemma : fpf-compatible-single-iff
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[x:A]. ∀[v:B[x]].
uiff(f || x : v;v = f(x) ∈ B[x] supposing ↑x ∈ dom(f))
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_wf,
fpf-compatible_wf,
fpf-single_wf,
fpf_ap_single_lemma,
fpf-dom_wf,
top_wf,
subtype-fpf2,
subtype_top,
isect_wf,
equal_wf,
fpf-ap_wf,
fpf_wf,
deq_wf,
fpf-single-dom,
fpf-single-dom-sq,
safe-assert-deq,
and_wf,
member_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
subtype_rel_self,
subtype_rel_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[x:A]. \mforall{}[v:B[x]].
uiff(f || x : v;v = f(x) supposing \muparrow{}x \mmember{} dom(f))
Date html generated:
2015_07_17-AM-11_12_56
Last ObjectModification:
2015_01_28-AM-07_43_41
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