Nuprl Lemma : fpf-compatible-singles-iff
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[x,y:A]. ∀[v:B[x]]. ∀[u:B[y]].
uiff(x : v || y : u;v = u ∈ B[x] supposing x = y ∈ A)
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
deq: EqDecider(T),
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 :
fpf_ap_single_lemma,
fpf-single-dom,
equal_wf,
fpf-compatible_wf,
fpf-single_wf,
fpf-compatible-singles,
assert_wf,
fpf-dom_wf,
top_wf,
isect_wf,
subtype_rel_self,
subtype_rel_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x,y:A]. \mforall{}[v:B[x]]. \mforall{}[u:B[y]].
uiff(x : v || y : u;v = u supposing x = y)
Date html generated:
2015_07_17-AM-11_13_01
Last ObjectModification:
2015_01_28-AM-07_43_18
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