Nuprl Lemma : unit_ss_point_lemma
Point(𝕀) ~ {x:ℝ| (r0 ≤ x) ∧ (x ≤ r1)}
Proof
Definitions occuring in Statement :
unit-ss: 𝕀,
ss-point: Point(ss),
rleq: x ≤ y,
int-to-real: r(n),
real: ℝ,
and: P ∧ Q,
set: {x:A| B[x]} ,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
and: P ∧ Q,
rccint: [l, u],
i-member: r ∈ I,
real: ℝ,
real-ss: ℝ,
btrue: tt,
bfalse: ff,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-update: r[x := v],
mk-ss: Point=P #=Sep symm=Sym cotrans=C,
set-ss: {x:ss | P[x]},
unit-ss: 𝕀,
record-select: r.x,
ss-point: Point(ss)
Rules used in proof :
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalRule,
sqequalSubstitution
Latex:
Point(\mBbbI{}) \msim{} \{x:\mBbbR{}| (r0 \mleq{} x) \mwedge{} (x \mleq{} r1)\}
Date html generated:
2018_07_29-AM-10_11_28
Last ObjectModification:
2018_06_29-AM-10_00_55
Theory : constructive!algebra
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