Nuprl Lemma : rat2real-qmax
∀[a,b:ℚ]. (rat2real(qmax(a;b)) = rmax(rat2real(a);rat2real(b)))
Proof
Definitions occuring in Statement :
rat2real: rat2real(q),
rmax: rmax(x;y),
req: x = y,
uall: ∀[x:A]. B[x],
qmax: qmax(x;y),
rationals: ℚ
Definitions unfolded in proof :
all: ∀x:A. B[x],
or: P ∨ Q,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
cand: A c∧ B,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
qle_connex,
qmax_ub,
qmax_lb,
qle_reflexivity,
rationals_wf,
req_witness,
rmax_wf,
req_fake_le_antisymmetry,
rleq-rat2real,
qle_wf,
rleq_wf,
iff_weakening_uiff,
rmax_lb,
qmax_wf,
rat2real_wf,
rmax_ub
Rules used in proof :
productIsType,
dependent_functionElimination,
unionElimination,
inrFormation_alt,
inlFormation_alt,
productEquality,
universeIsType,
isectIsTypeImplies,
isect_memberEquality_alt,
sqequalRule,
inhabitedIsType,
promote_hyp,
independent_functionElimination,
productElimination,
because_Cache,
independent_pairFormation,
independent_isectElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:\mBbbQ{}]. (rat2real(qmax(a;b)) = rmax(rat2real(a);rat2real(b)))
Date html generated:
2019_10_31-AM-05_57_51
Last ObjectModification:
2019_10_30-PM-06_54_48
Theory : reals
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