Nuprl Lemma : arcsin-minus1
arcsin(r(-1)) = -(π/2)
Proof
Definitions occuring in Statement :
arcsin: arcsin(a),
halfpi: π/2,
req: x = y,
rminus: -(x),
int-to-real: r(n),
minus: -n,
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
prop: ℙ,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
top: Top,
subtype_rel: A ⊆r B,
req_int_terms: t1 ≡ t2,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
rminus_wf,
int-to-real_wf,
rleq_weakening,
rleq_wf,
itermSubtract_wf,
itermConstant_wf,
itermMinus_wf,
req-iff-rsub-is-0,
rleq-int,
istype-false,
arcsin_wf,
member_rccint_lemma,
istype-void,
rleq_weakening_equal,
halfpi_wf,
real_polynomial_null,
istype-int,
real_term_value_sub_lemma,
real_term_value_const_lemma,
real_term_value_minus_lemma,
rleq_functionality,
req_weakening,
req_functionality,
rminus_functionality,
req_inversion,
arcsin1,
arcsin-rminus,
arcsin_functionality
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality_alt,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
minusEquality,
because_Cache,
independent_isectElimination,
independent_pairFormation,
sqequalRule,
productIsType,
universeIsType,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_functionElimination,
independent_functionElimination,
lambdaFormation_alt,
isect_memberEquality_alt,
voidElimination,
applyEquality,
approximateComputation,
lambdaEquality_alt
Latex:
arcsin(r(-1)) = -(\mpi{}/2)
Date html generated:
2019_10_31-AM-06_15_30
Last ObjectModification:
2019_05_24-PM-04_40_33
Theory : reals_2
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