Nuprl Lemma : req-rat2real
∀q1,q2:ℚ. uiff(rat2real(q1) = rat2real(q2);q1 = q2 ∈ ℚ)
Proof
Definitions occuring in Statement :
rat2real: rat2real(q),
req: x = y,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
equal: s = t ∈ T,
rationals: ℚ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
or: P ∨ Q,
decidable: Dec(P),
not: ¬A,
false: False
Latex:
\mforall{}q1,q2:\mBbbQ{}. uiff(rat2real(q1) = rat2real(q2);q1 = q2)
Date html generated:
2020_05_20-AM-11_01_16
Last ObjectModification:
2020_01_06-PM-00_26_37
Theory : reals
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