Nuprl Lemma : rat2real_wf
∀[q:ℚ]. (rat2real(q) ∈ ℝ)
Proof
Definitions occuring in Statement :
rat2real: rat2real(q),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rationals: ℚ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rationals: ℚ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
rat2real: rat2real(q),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
btrue: tt,
qeq: qeq(r;s),
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
real: ℝ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
int_nzero: ℤ-o,
int-to-real: r(n),
int-rdiv: (a)/k1,
nequal: a ≠ b ∈ T ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[q:\mBbbQ{}]. (rat2real(q) \mmember{} \mBbbR{})
Date html generated:
2020_05_20-AM-11_01_05
Last ObjectModification:
2019_12_28-PM-08_14_41
Theory : reals
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