Nuprl Lemma : rsub-int-fractions
∀[a,b:ℤ]. ∀[c,d:ℕ+]. (((r(a)/r(c)) - (r(b)/r(d))) = (r((a * d) - b * c)/r(c * d)))
Proof
Definitions occuring in Statement :
rdiv: (x/y),
rsub: x - y,
req: x = y,
int-to-real: r(n),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
multiply: n * m,
subtract: 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,
true: True,
subtract: n - m,
squash: ↓T,
subtype_rel: A ⊆r B,
rsub: x - y,
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 * d) - b * c)/r(c * d)))
Date html generated:
2020_05_20-AM-11_00_43
Last ObjectModification:
2020_01_03-AM-11_17_22
Theory : reals
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