Nuprl Lemma : req-int
∀[a,b:ℤ]. uiff(r(a) = r(b);a = b ∈ ℤ)
Proof
Definitions occuring in Statement :
req: x = y,
int-to-real: r(n),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than': less_than'(a;b),
less_than: a < b,
nat_plus: ℕ+,
all: ∀x:A. B[x],
req: x = y,
int-to-real: r(n),
top: Top,
subtract: n - m,
or: P ∨ Q,
decidable: Dec(P),
not: ¬A,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Latex:
\mforall{}[a,b:\mBbbZ{}]. uiff(r(a) = r(b);a = b)
Date html generated:
2020_05_20-AM-10_53_25
Last ObjectModification:
2020_01_06-PM-00_27_43
Theory : reals
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