Nuprl Lemma : qmax-imax
∀[x,y:ℤ]. (qmax(x;y) ~ imax(x;y))
Proof
Definitions occuring in Statement :
qmax: qmax(x;y),
imax: imax(a;b),
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
imax: imax(a;b),
qmax: qmax(x;y),
q_le: q_le(r;s),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
decidable: Dec(P)
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
valueall-type-has-valueall,
int-valueall-type,
evalall-reduce,
value-type-has-value,
int-value-type,
qsub-sub,
qpositive_wf,
subtract_wf,
bool_wf,
eqtt_to_assert,
assert-qpositive,
int-subtype-rationals,
qless-int,
le_int_wf,
assert_of_le_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
le_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformnot_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
qless_wf,
less_than_wf,
assert-qeq,
equal-wf-base,
rationals_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
qeq_wf2,
int-equal-in-rationals
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
hypothesisEquality,
callbyvalueReduce,
because_Cache,
applyEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
natural_numberEquality,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
sqequalAxiom
Latex:
\mforall{}[x,y:\mBbbZ{}]. (qmax(x;y) \msim{} imax(x;y))
Date html generated:
2018_05_21-PM-11_52_24
Last ObjectModification:
2017_07_26-PM-06_45_03
Theory : rationals
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