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) 
(v = u)
Proof not projected
Definitions occuring in Statement :
fpf-single: x : v,
fpf-compatible: f || g,
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,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
so_apply: x[s],
uimplies: b supposing a,
implies: P Q,
fpf-compatible: f || g,
member: t 
T,
all: x:A. B[x],
and: P 
Q,
prop: 
,
top: Top,
so_lambda: 
x.t[x],
ifthenelse: if b then t else f fi ,
guard: {T},
bfalse: ff,
assert: 
b,
eqof: eqof(d),
reduce: reduce(f;k;as),
pi1: fst(t),
deq-member: deq-member(eq;x;L),
fpf-dom: x dom(f),
fpf-single: x : v,
iff: P 
Q,
false: False,
or: P 
Q,
deq: EqDecider(T)
Lemmas :
and_wf,
assert_wf,
fpf-dom_wf,
fpf-single_wf,
top_wf,
equal_wf,
deq_wf,
assert-deq,
or_functionality_wrt_uiff2,
assert_of_bor,
iff_weakening_uiff,
iff_transitivity,
false_wf,
or_wf,
bfalse_wf,
bor_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]].
x : v || y : u supposing (x = y) {}\mRightarrow{} (v = u)
Date html generated:
2012_01_23-AM-11_55_22
Last ObjectModification:
2011_12_10-PM-12_07_38
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