Nuprl Lemma : qmin-list-member
∀L:ℚ List. (qmin-list(L) ∈ L) supposing 0 < ||L||
Proof
Definitions occuring in Statement :
qmin-list: qmin-list(L),
rationals: ℚ,
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
qmin-list: qmin-list(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
qmin: qmin(x;y),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
or: P ∨ Q,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
member-less_than,
length_wf,
rationals_wf,
combine-list-member,
qmin_wf,
q_le_wf,
bool_wf,
eqtt_to_assert,
equal_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_isectElimination,
rename,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
independent_functionElimination,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
inlFormation,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
because_Cache,
voidElimination,
inrFormation
Latex:
\mforall{}L:\mBbbQ{} List. (qmin-list(L) \mmember{} L) supposing 0 < ||L||
Date html generated:
2018_05_21-PM-11_50_22
Last ObjectModification:
2017_07_26-PM-06_44_00
Theory : rationals
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