Nuprl Lemma : fpf-all-single
[A:Type]
eq:EqDecider(A)
[B:A 
Type]. [P:x:A B[x] 
]. x:A. v:B[x]. (y
dom(x : v). w=x : v(y) 
P[y;w] 
P[x;v])
Proof not projected
Definitions occuring in Statement :
fpf-all: xdom(f). v=f(x) P[x; v],
fpf-single: x : v,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
function: x:A B[x],
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
so_apply: x[s],
prop: ,
fpf-all: xdom(f). v=f(x) P[x; v],
fpf-single: x : v,
fpf-dom: x dom(f),
fpf-ap: f(x),
deq-member: deq-member(eq;x;L),
pi1: fst(t),
pi2: snd(t),
reduce: reduce(f;k;as),
member: t T,
iff: P Q,
implies: P Q,
so_apply: x[s1;s2],
and: P 
Q,
rev_implies: P Q,
so_lambda: 
x.t[x],
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
bor: p 
q,
assert: 
b,
guard: {T},
bfalse: ff,
false: False,
or: P Q,
eqof: eqof(d),
deq: EqDecider(T)
Lemmas :
deq_wf,
all_wf,
assert_wf,
bor_wf,
eqof_wf,
bfalse_wf,
eqof_eq_btrue,
and_wf,
assert-deq,
or_functionality_wrt_uiff2,
assert_of_bor,
iff_weakening_uiff,
iff_transitivity,
false_wf,
equal_wf,
or_wf
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[P:x:A {}\mrightarrow{} B[x] {}\mrightarrow{} \mBbbP{}].
\mforall{}x:A. \mforall{}v:B[x]. (\mforall{}y\mmember{}dom(x : v). w=x : v(y) {}\mRightarrow{} P[y;w] \mLeftarrow{}{}\mRightarrow{} P[x;v])
Date html generated:
2012_01_23-AM-11_55_45
Last ObjectModification:
2011_12_10-PM-12_34_28
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