Nuprl Lemma : IVT-test
∃x:ℝ [(x^3 = r(2))]
Proof
Definitions occuring in Statement :
rnexp: x^k1,
req: x = y,
int-to-real: r(n),
real: ℝ,
sq_exists: ∃x:A [B[x]],
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
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,
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
rneq: x ≠ y,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
le: A ≤ B,
exp: i^n,
primrec: primrec(n;b;c),
subtract: n - m,
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
sq_exists: ∃x:A [B[x]]
Lemmas referenced :
rational-fun-zero_wf,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
ratsub_wf,
ratexp_wf,
decidable__le,
intformle_wf,
int_formula_prop_le_lemma,
istype-le,
nat_plus_wf,
rsub_wf,
rnexp_wf,
int-to-real_wf,
real_wf,
i-member_wf,
rccint_wf,
ratreal_wf,
req_functionality,
rsub_functionality,
rnexp_functionality,
req_weakening,
req_wf,
rdiv_wf,
rless-int,
rless_wf,
rleq-int-fractions,
istype-false,
radd_wf,
rmul_wf,
rinv_wf2,
itermSubtract_wf,
itermVar_wf,
itermMultiply_wf,
itermAdd_wf,
exp_wf2,
rleq-int,
rleq_functionality,
ratreal-req,
req_transitivity,
ratreal-ratsub,
ratreal-ratexp,
radd_functionality,
rmul_functionality,
rinv1,
rmul-identity1,
rmul-int,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_var_lemma,
real_term_value_mul_lemma,
real_term_value_const_lemma,
real_term_value_add_lemma,
rnexp-int,
radd-int,
member_rccint_lemma,
subtype_rel_sets_simple,
rleq_wf,
req-implies-req
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
independent_pairEquality,
natural_numberEquality,
dependent_set_memberEquality_alt,
hypothesis,
unionElimination,
isectElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
universeIsType,
hypothesisEquality,
applyEquality,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
productIsType,
setIsType,
independent_pairFormation,
lambdaFormation_alt,
because_Cache,
productElimination,
closedConclusion,
inrFormation_alt,
imageMemberEquality,
baseClosed,
minusEquality,
multiplyEquality,
addEquality,
int_eqEquality,
productEquality
Latex:
\mexists{}x:\mBbbR{} [(x\^{}3 = r(2))]
Date html generated:
2019_10_30-AM-10_02_26
Last ObjectModification:
2019_01_11-PM-05_34_56
Theory : reals
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