Nuprl Lemma : fpf-compatible-singles
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[x,y:A]. ∀[v:B[x]]. ∀[u:B[y]].
x : v || y : u supposing (x = y ∈ A) ⇒ (v = u ∈ B[x])
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_wf,
fpf-dom_wf,
fpf-single_wf,
top_wf,
subtype_rel_self,
subtype_rel_wf,
deq_wf,
fpf_ap_pair_lemma,
deq_member_cons_lemma,
deq_member_nil_lemma,
bor_wf,
bfalse_wf,
eqof_wf,
or_wf,
equal_wf,
false_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bor,
safe-assert-deq,
equal_functionality_wrt_subtype_rel2
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x,y:A]. \mforall{}[v:B[x]]. \mforall{}[u:B[y]].
x : v || y : u supposing (x = y) {}\mRightarrow{} (v = u)
Date html generated:
2015_07_17-AM-11_12_37
Last ObjectModification:
2015_01_28-AM-07_43_13
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