Nuprl Lemma : rstar-rmul
∀[x,y:ℝ]. (x)* * (y)* = (x * y)*
Proof
Definitions occuring in Statement :
rstar: (x)*,
rmul*: x * y,
req*: x = y,
rmul: a * b,
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],
rstar: (x)*,
rmul*: x * y,
rfun*2: f*(x;y),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
false_wf,
le_wf,
req_weakening,
rmul_wf,
int_upper_wf,
all_wf,
req_wf,
rmul*_wf,
rstar_wf,
int_upper_subtype_nat,
real_wf
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,
because_Cache,
independent_isectElimination,
setElimination,
rename,
lambdaEquality,
applyEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. (x)* * (y)* = (x * y)*
Date html generated:
2018_05_22-PM-03_18_40
Last ObjectModification:
2017_10_06-PM-06_25_14
Theory : reals_2
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