Nuprl Lemma : rmax-req
∀[x,y:ℝ]. rmax(x;y) = y supposing x ≤ y
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rmax: rmax(x;y),
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
nat_plus: ℕ+,
prop: ℙ,
so_lambda: λ2x.t[x],
int_upper: {i...},
real: ℝ,
le: A ≤ B,
guard: {T},
subtype_rel: A ⊆r B,
so_apply: x[s],
rmax: rmax(x;y),
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
squash: ↓T
Lemmas referenced :
rleq_antisymmetry,
rmax_wf,
rleq-iff,
int_upper_wf,
all_wf,
le_wf,
subtract_wf,
less_than_transitivity1,
less_than_wf,
nat_plus_wf,
rleq-rmax,
req_witness,
rleq_wf,
real_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
int_upper_properties,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
itermSubtract_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
squash_wf,
true_wf,
imax_unfold,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
lambdaFormation,
dependent_pairFormation,
setElimination,
rename,
sqequalRule,
lambdaEquality,
multiplyEquality,
minusEquality,
natural_numberEquality,
applyEquality,
dependent_set_memberEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
unionElimination,
equalityElimination,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
promote_hyp,
instantiate,
cumulativity,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. rmax(x;y) = y supposing x \mleq{} y
Date html generated:
2017_10_03-AM-08_30_05
Last ObjectModification:
2017_07_28-AM-07_26_20
Theory : reals
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