Nuprl Lemma : ravg_comm
∀[x,y:ℝ]. (ravg(x;y) = ravg(y;x))
Proof
Definitions occuring in Statement :
ravg: ravg(x;y),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
top: Top,
not: ¬A,
false: False,
req_int_terms: t1 ≡ t2,
rdiv: (x/y),
true: True,
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b,
rev_uimplies: rev_uimplies(P;Q),
uiff: uiff(P;Q),
prop: ℙ,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
guard: {T},
rneq: x ≠ y,
uimplies: b supposing a,
ravg: ravg(x;y),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real_term_value_const_lemma,
real_term_value_var_lemma,
real_term_value_add_lemma,
real_term_value_mul_lemma,
real_term_value_sub_lemma,
real_polynomial_null,
rmul-rinv3,
radd_functionality,
req_transitivity,
req_functionality,
req_weakening,
req-iff-rsub-is-0,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
itermMultiply_wf,
itermSubtract_wf,
rinv_wf2,
rless_wf,
int-to-real_wf,
radd_wf,
rmul_wf,
real_wf,
ravg_wf,
req_witness,
rless-int,
rdiv_wf,
rmul_preserves_req
Rules used in proof :
voidEquality,
voidElimination,
intEquality,
int_eqEquality,
lambdaEquality,
approximateComputation,
baseClosed,
imageMemberEquality,
independent_pairFormation,
natural_numberEquality,
isect_memberEquality,
hypothesisEquality,
independent_functionElimination,
productElimination,
dependent_functionElimination,
inrFormation,
hypothesis,
sqequalRule,
independent_isectElimination,
because_Cache,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[x,y:\mBbbR{}]. (ravg(x;y) = ravg(y;x))
Date html generated:
2017_10_03-AM-08_41_44
Last ObjectModification:
2017_07_31-AM-10_31_17
Theory : reals
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