Nuprl Lemma : half-pi_wf
π/2(slower) ∈ ℝ
Proof
Definitions occuring in Statement :
half-pi: π/2(slower),
real: ℝ,
member: t ∈ T
Definitions unfolded in proof :
half-pi: π/2(slower),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
nat_plus: ℕ+,
has-value: (a)↓,
all: ∀x:A. B[x],
int_upper: {i...},
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
ge: i ≥ j ,
uiff: uiff(P;Q),
real: ℝ,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
converges: x[n]↓ as n→∞,
pi1: fst(t),
rcos-seq-converges-ext,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
nat_plus_wf,
value-type-has-value,
int-value-type,
exp-ratio_wf2,
false_wf,
le_wf,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
less_than_wf,
rcos-seq_wf,
add_nat_wf,
nat_wf,
nat_properties,
add-is-int-iff,
itermAdd_wf,
intformeq_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
equal_wf,
real_wf,
decidable__equal_int,
decidable__lt,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
rcos-seq-converges-ext,
converges_wf,
pi1_wf_top,
regular-int-seq_wf,
squash_wf,
iff_weakening_equal
Rules used in proof :
cut,
functionExtensionality,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
multiplyEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
callbyvalueReduce,
because_Cache,
addEquality,
dependent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageMemberEquality,
baseClosed,
applyEquality,
divideEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
productElimination,
independent_functionElimination,
addLevel,
instantiate,
cumulativity,
independent_pairEquality,
imageElimination,
functionEquality,
universeEquality
Latex:
\mpi{}/2(slower) \mmember{} \mBbbR{}
Date html generated:
2017_10_04-PM-10_24_04
Last ObjectModification:
2017_07_28-AM-08_48_45
Theory : reals_2
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