Nuprl Lemma : rabs-rnexp2
∀[x:ℝ]. (|x|^2 = x^2)
Proof
Definitions occuring in Statement :
rabs: |x|,
rnexp: x^k1,
req: x = y,
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),
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rnexp_wf,
istype-void,
istype-le,
rabs_wf,
real_wf,
rnexp2-nonneg,
req_weakening,
req_functionality,
req_inversion,
rabs-rnexp,
rabs-of-nonneg
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation_alt,
voidElimination,
hypothesis,
hypothesisEquality,
independent_functionElimination,
universeIsType,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x:\mBbbR{}]. (|x|\^{}2 = x\^{}2)
Date html generated:
2019_10_29-AM-09_39_50
Last ObjectModification:
2019_06_25-PM-02_02_31
Theory : reals
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