Nuprl Lemma : rpower-two
∀[x:ℝ]. (x^2 = (x * x))
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
rmul: a * b,
real: ℝ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[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
Lemmas referenced :
rnexp2,
req_witness,
rnexp_wf,
false_wf,
le_wf,
rmul_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbR{}]. (x\^{}2 = (x * x))
Date html generated:
2016_05_18-AM-07_20_16
Last ObjectModification:
2015_12_28-AM-00_47_25
Theory : reals
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