Nuprl Lemma : rsqrt_2-irrational
irrational(rsqrt(r(2)))
This theorem is one of freek's list of 100 theorems
Proof
Definitions occuring in Statement :
irrational: irrational(x),
rsqrt: rsqrt(x),
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
or: P ∨ Q,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
member: t ∈ T,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
true: True,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
int_seg_subtype,
false_wf,
int_seg_cases,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
rsqrt-irrational,
le_wf
Rules used in proof :
unionElimination,
hypothesisEquality,
isectElimination,
hypothesis,
lambdaFormation,
independent_pairFormation,
sqequalRule,
natural_numberEquality,
dependent_set_memberEquality,
thin,
dependent_functionElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
lemma_by_obid,
cut,
productElimination,
introduction,
extract_by_obid,
setElimination,
rename,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
voidElimination,
promote_hyp,
hypothesis_subsumption,
addEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
irrational(rsqrt(r(2)))
Date html generated:
2016_10_26-AM-11_11_43
Last ObjectModification:
2016_09_07-PM-11_56_02
Theory : reals
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