Nuprl Lemma : fpf-compatible-triple
[T:Type]. [eq:EqDecider(T)]. [f,g,h:x:T fp-> Type].
({(g 
h 
f g 
f h f g) h g h f g h f h f g}) supposing (h || g and h || f and f || g)
Proof not projected
Definitions occuring in Statement :
fpf-join: f g,
fpf-compatible: f || g,
fpf-sub: f g,
fpf: a:A fp-> B[a],
uimplies: b supposing a,
uall: [x:A]. B[x],
guard: {T},
and: P Q,
universe: Type,
deq: EqDecider(T)
Definitions :
uall: [x:A]. B[x],
uimplies: b supposing a,
guard: {T},
and: P Q,
fpf-sub: f g,
member: t 
T,
all: x:A. B[x],
implies: P 
Q,
cand: A c B,
so_lambda: 
x.t[x],
assert: 
b,
prop: 
,
top: Top,
or: P 
Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
true: True,
rev_implies: P 
Q,
iff: P Q,
bfalse: ff,
so_apply: x[s],
fpf-compatible: f || g,
sq_type: SQType(T),
false: False,
not: 
A,
bool: 
,
unit: Unit,
it: 
Lemmas :
pair_wf,
assert_wf,
fpf-dom_wf,
fpf-join_wf,
top_wf,
fpf-trivial-subtype-top,
assert_witness,
fpf-compatible_wf,
fpf_wf,
deq_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_elim,
not_wf,
bnot_wf,
fpf-ap_wf,
fpf-join-dom2,
iff_transitivity,
or_functionality_wrt_iff,
fpf-join-ap-sq,
iff_weakening_uiff,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[f,g,h:x:T fp-> Type].
(\{(g \msubseteq{} h \moplus{} f \moplus{} g \mwedge{} f \msubseteq{} h \moplus{} f \moplus{} g) \mwedge{} h \moplus{} g \msubseteq{} h \moplus{} f \moplus{} g \mwedge{} h \moplus{} f \msubseteq{} h \moplus{} f \moplus{} g\}) supposing
(h || g and
h || f and
f || g)
Date html generated:
2012_01_23-AM-11_55_55
Last ObjectModification:
2011_12_27-PM-11_22_22
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