Nuprl Lemma : rnexp3
∀[x:ℝ]. (x^3 = (x * 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,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
subtract: n - m,
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rnexp_wf,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
rmul_wf,
real_wf,
ifthenelse_wf,
eq_int_wf,
int-to-real_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
rmul_assoc,
req_functionality,
rnexp_unroll,
req_weakening,
rmul_functionality,
rnexp2
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,
dependent_functionElimination,
hypothesis,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
universeIsType,
hypothesisEquality,
because_Cache,
productElimination
Latex:
\mforall{}[x:\mBbbR{}]. (x\^{}3 = (x * x * x))
Date html generated:
2019_10_29-AM-09_39_31
Last ObjectModification:
2019_02_02-PM-02_21_47
Theory : reals
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