Nuprl Lemma : rat2real-qmul
∀[a,b:ℚ]. (rat2real(a * b) = (rat2real(a) * rat2real(b)))
Proof
Definitions occuring in Statement :
rat2real: rat2real(q),
req: x = y,
rmul: a * b,
uall: ∀[x:A]. B[x],
qmul: r * s,
rationals: ℚ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
nat_plus: ℕ+,
cand: A c∧ B,
not: ¬A,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
uimplies: b supposing a,
mk-rational: mk-rational(a;b),
qmul: r * s,
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
ifthenelse: if b then t else f fi ,
bfalse: ff,
rat2real: rat2real(q),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[a,b:\mBbbQ{}]. (rat2real(a * b) = (rat2real(a) * rat2real(b)))
Date html generated:
2020_05_20-AM-11_01_39
Last ObjectModification:
2020_01_02-PM-02_12_16
Theory : reals
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