Nuprl Lemma : inhabited-rat-point-interval
∀[a:ℚ]. (Inhabited([a]) ~ tt)
Proof
Definitions occuring in Statement :
inhabited-rat-interval: Inhabited(I),
rat-point-interval: [a],
rationals: ℚ,
btrue: tt,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
sq_type: SQType(T),
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
prop: ℙ,
squash: ↓T,
rat-point-interval: [a],
inhabited-rat-interval: Inhabited(I),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rationals_wf,
istype-true,
qle_reflexivity,
qle_wf,
iff_weakening_equal,
subtype_rel_self,
assert-q_le-eq,
true_wf,
squash_wf,
iff_wf,
q_le_wf,
iff_imp_equal_bool,
bool_subtype_base,
bool_wf,
subtype_base_sq
Rules used in proof :
axiomSqEquality,
dependent_functionElimination,
lambdaFormation_alt,
independent_pairFormation,
independent_functionElimination,
productElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
universeEquality,
inhabitedIsType,
universeIsType,
equalitySymmetry,
equalityTransitivity,
imageElimination,
lambdaEquality_alt,
applyEquality,
because_Cache,
hypothesisEquality,
sqequalRule,
independent_isectElimination,
hypothesis,
cumulativity,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a:\mBbbQ{}]. (Inhabited([a]) \msim{} tt)
Date html generated:
2019_10_29-AM-07_47_43
Last ObjectModification:
2019_10_17-PM-05_01_15
Theory : rationals
Home
Index