Nuprl Lemma : qmax-assoc
∀[x,y,z:ℚ]. (qmax(qmax(x;y);z) = qmax(x;qmax(y;z)) ∈ ℚ)
Proof
Definitions occuring in Statement :
qmax: qmax(x;y),
rationals: ℚ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qmax: qmax(x;y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
not: ¬A
Lemmas referenced :
q_le_wf,
bool_wf,
eqtt_to_assert,
assert-q_le-eq,
iff_weakening_equal,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
not_wf,
qle_transitivity_qorder,
squash_wf,
true_wf,
qle_complement_qorder,
qless_transitivity_2_qorder,
qless_transitivity,
qless_irreflexivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
because_Cache,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
voidElimination,
applyEquality,
lambdaEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[x,y,z:\mBbbQ{}]. (qmax(qmax(x;y);z) = qmax(x;qmax(y;z)))
Date html generated:
2018_05_21-PM-11_55_27
Last ObjectModification:
2017_07_26-PM-06_46_13
Theory : rationals
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