Nuprl Lemma : rat2real-qmin
∀[a,b:ℚ]. (rat2real(qmin(a;b)) = rmin(rat2real(a);rat2real(b)))
Proof
Definitions occuring in Statement :
rat2real: rat2real(q),
rmin: rmin(x;y),
req: x = y,
uall: ∀[x:A]. B[x],
qmin: qmin(x;y),
rationals: ℚ
Definitions unfolded in proof :
prop: ℙ,
or: P ∨ Q,
guard: {T},
uimplies: b supposing a,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
qle_connex,
qmin_ub,
qmin_lb,
qle_reflexivity,
rationals_wf,
req_witness,
rmin_wf,
req_fake_le_antisymmetry,
rmin_lb,
rleq-rat2real,
qle_wf,
rleq_wf,
iff_weakening_uiff,
qmin_wf,
rat2real_wf,
rmin_ub
Rules used in proof :
productIsType,
unionElimination,
productEquality,
inrFormation_alt,
inlFormation_alt,
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
sqequalRule,
inhabitedIsType,
independent_isectElimination,
because_Cache,
promote_hyp,
independent_pairFormation,
independent_functionElimination,
productElimination,
hypothesis,
hypothesisEquality,
isectElimination,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:\mBbbQ{}]. (rat2real(qmin(a;b)) = rmin(rat2real(a);rat2real(b)))
Date html generated:
2019_10_31-AM-05_58_02
Last ObjectModification:
2019_10_30-PM-06_56_59
Theory : reals
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