Nuprl Lemma : monus_le
a,b,c:
. ((a 
b) 
((a--c) (b--c)))
Proof
Definitions occuring in Statement :
monus: (a--b),
nat: ,
le: A B,
all: x:A. B[x],
implies: P Q
Definitions :
all: x:A. B[x],
nat: ,
implies: P Q,
le: A B,
monus: (a--b),
ifthenelse: if b then t else f fi ,
member: t 
T,
btrue: tt,
not: 
A,
false: False,
bfalse: ff,
exists: 
x:A. B[x],
bool: 
,
uall: [x:A]. B[x],
unit: Unit,
uimplies: b supposing a,
assert: 
b,
uiff: uiff(P;Q),
and: P 
Q,
prop: 
,
bnot: 
b,
or: P 
Q,
sq_type: SQType(T),
guard: {T},
it: 
Lemmas :
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
Error :zero-le-nat,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
Error :assert-bnot,
less_than_wf,
nat_wf
\mforall{}a,b,c:\mBbbN{}. ((a \mleq{} b) {}\mRightarrow{} ((a--c) \mleq{} (b--c)))
Date html generated:
2013_03_20-AM-10_38_02
Last ObjectModification:
2013_03_18-PM-04_44_00
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