Nuprl Lemma : extensional-real-to-bool-constant
āf:ā ā¶ š¹. āx,y:ā. f x = f y supposing āx,y:ā. ((x = y)
ā f x = f y)
Proof
Definitions occuring in Statement :
req: x = y
,
real: ā
,
bool: š¹
,
uimplies: b supposing a
,
all: āx:A. B[x]
,
implies: P
ā Q
,
apply: f a
,
function: x:A ā¶ B[x]
,
equal: s = t ā T
Definitions unfolded in proof :
all: āx:A. B[x]
,
uimplies: b supposing a
,
member: t ā T
,
decidable: Dec(P)
,
or: P āØ Q
,
not: Ā¬A
,
implies: P
ā Q
,
true: True
,
false: False
,
uall: ā[x:A]. B[x]
,
prop: ā
,
so_lambda: Ī»2x.t[x]
,
guard: {T}
,
sq_type: SQType(T)
,
cand: A cā§ B
,
and: P ā§ Q
,
top: Top
,
bfalse: ff
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
uiff: uiff(P;Q)
,
iff: P
āā Q
Latex:
\mforall{}f:\mBbbR{} {}\mrightarrow{} \mBbbB{}. \mforall{}x,y:\mBbbR{}. f x = f y supposing \mforall{}x,y:\mBbbR{}. ((x = y) {}\mRightarrow{} f x = f y)
Date html generated:
2020_05_20-PM-00_05_12
Last ObjectModification:
2020_01_09-PM-06_15_14
Theory : reals
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