Nuprl Lemma : assert-inhabited-rat-interval
∀[I:ℚInterval]. uiff(↑Inhabited(I);(fst(I)) ≤ (snd(I)))
Proof
Definitions occuring in Statement :
inhabited-rat-interval: Inhabited(I),
rational-interval: ℚInterval,
qle: r ≤ s,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t)
Definitions unfolded in proof :
top: Top,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
prop: ℙ,
implies: P ⇒ Q,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
pi2: snd(t),
pi1: fst(t),
inhabited-rat-interval: Inhabited(I),
rational-interval: ℚInterval,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rational-interval_wf,
inhabited-rat-interval_wf,
istype-void,
rationals_wf,
pi1_wf_top,
assert_witness,
q_le_wf,
istype-assert,
iff_weakening_equal,
assert-q_le-eq,
qle_wf,
qle_witness
Rules used in proof :
inhabitedIsType,
isectIsTypeImplies,
voidElimination,
isect_memberEquality_alt,
independent_pairEquality,
promote_hyp,
equalitySymmetry,
equalityTransitivity,
independent_isectElimination,
because_Cache,
universeIsType,
independent_functionElimination,
hypothesisEquality,
isectElimination,
extract_by_obid,
hypothesis,
independent_pairFormation,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[I:\mBbbQ{}Interval]. uiff(\muparrow{}Inhabited(I);(fst(I)) \mleq{} (snd(I)))
Date html generated:
2019_10_29-AM-07_47_37
Last ObjectModification:
2019_10_17-PM-04_33_46
Theory : rationals
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