Nuprl Lemma : pi-positive
r0 < π
Proof
Definitions occuring in Statement :
pi: π,
rless: x < y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
pi: π,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
uimplies: b supposing a,
itermConstant: "const",
req_int_terms: t1 ≡ t2,
top: Top,
uiff: uiff(P;Q),
false: False,
not: ¬A
Lemmas referenced :
int-to-real_wf,
int-rmul_wf,
halfpi_wf,
rmul_wf,
halfpi-positive,
rmul_preserves_rless,
rless-int,
rless_functionality,
real_term_polynomial,
itermSubtract_wf,
itermMultiply_wf,
itermConstant_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_mul_lemma,
req-iff-rsub-is-0,
itermVar_wf,
real_term_value_var_lemma,
req_weakening,
int-rmul-req
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
productElimination,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
independent_isectElimination,
computeAll,
lambdaEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
int_eqEquality
Latex:
r0 < \mpi{}
Date html generated:
2017_10_04-PM-10_25_23
Last ObjectModification:
2017_07_28-AM-08_49_08
Theory : reals_2
Home
Index