Nuprl Lemma : halfpi_wf1
π/2 ∈ {x:ℝ| x = π/2(slower)}
Proof
Definitions occuring in Statement :
halfpi: π/2,
half-pi: π/2(slower),
req: x = y,
real: ℝ,
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_apply: x[s],
fastpi-converges-ext,
cauchy-limit: cauchy-limit(n.x[n];c),
halfpi: π/2,
accelerate: accelerate(k;f),
uimplies: b supposing a,
nat_plus: ℕ+,
has-value: (a)↓,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
subtype_rel: A ⊆r B,
real: ℝ,
true: True,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
guard: {T},
squash: ↓T
Lemmas referenced :
req-from-converges,
fastpi_wf,
nat_wf,
half-pi_wf,
fastpi-converges-ext,
nat_plus_wf,
value-type-has-value,
int-value-type,
le_wf,
exp_wf2,
exp_wf4,
false_wf,
set-value-type,
cubic_converge_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,
real_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__lt,
less_than_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
cauchy-limit_wf,
converges-cauchy-witness,
regular-int-seq_wf,
req_inversion,
req_transitivity,
req_weakening,
req_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
instantiate,
functionExtensionality,
callbyvalueReduce,
sqleReflexivity,
intEquality,
independent_isectElimination,
multiplyEquality,
natural_numberEquality,
setElimination,
rename,
because_Cache,
setEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
divideEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
addLevel,
cumulativity,
independent_functionElimination,
baseClosed,
Error :applyLambdaEquality,
imageMemberEquality,
imageElimination
Latex:
\mpi{}/2 \mmember{} \{x:\mBbbR{}| x = \mpi{}/2(slower)\}
Date html generated:
2016_10_26-PM-00_22_54
Last ObjectModification:
2016_09_12-PM-05_42_38
Theory : reals_2
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