Nuprl Lemma : standard-fact-example1
∀[x,y,z:ℝ*]. x * y * z = z * y * x
Proof
Definitions occuring in Statement :
rmul*: x * y,
req*: x = y,
real*: ℝ*,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
req*: x = y,
exists: ∃x:A. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
rmul*: x * y,
rfun*2: f*(x;y),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
real*: ℝ*,
int_upper: {i...},
uiff: uiff(P;Q),
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
top: Top
Lemmas referenced :
false_wf,
le_wf,
int_upper_wf,
all_wf,
req_wf,
rmul*_wf,
int_upper_subtype_nat,
real*_wf,
rmul_wf,
subtype_rel_self,
nat_wf,
rmul_assoc,
itermSubtract_wf,
itermMultiply_wf,
itermVar_wf,
req-iff-rsub-is-0,
req_weakening,
req_functionality,
real_polynomial_null,
int-to-real_wf,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
because_Cache,
lambdaEquality,
applyEquality,
productElimination,
independent_isectElimination,
dependent_functionElimination,
approximateComputation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[x,y,z:\mBbbR{}*]. x * y * z = z * y * x
Date html generated:
2018_05_22-PM-03_17_14
Last ObjectModification:
2017_10_06-PM-03_55_01
Theory : reals_2
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