Nuprl Lemma : rmul-int-fractions
∀[a,b:ℤ]. ∀[c,d:ℕ+]. (((r(a)/r(c)) * (r(b)/r(d))) = (r(a * b)/r(c * d)))
Proof
Definitions occuring in Statement :
rdiv: (x/y),
req: x = y,
rmul: a * b,
int-to-real: r(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
multiply: n * m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
nequal: a ≠ b ∈ T ,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[a,b:\mBbbZ{}]. \mforall{}[c,d:\mBbbN{}\msupplus{}]. (((r(a)/r(c)) * (r(b)/r(d))) = (r(a * b)/r(c * d)))
Date html generated:
2020_05_20-AM-11_00_54
Last ObjectModification:
2020_01_02-PM-02_12_40
Theory : reals
Home
Index