Nuprl Lemma : rsin-half-pi
rsin(π/2(slower)) = r1
Proof
Definitions occuring in Statement :
half-pi: π/2(slower),
rsin: rsin(x),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
true: True,
uimplies: b supposing a,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rneq: x ≠ y,
or: P ∨ Q,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
subtype_rel: A ⊆r B,
real: ℝ
Lemmas referenced :
rsin-rcos-pythag,
half-pi_wf,
radd_wf,
rnexp_wf,
false_wf,
le_wf,
rsin_wf,
rcos_wf,
int-to-real_wf,
less_than_wf,
req_wf,
req_functionality,
radd_functionality,
rnexp_functionality,
rcos-half-pi,
req_weakening,
rnexp0,
uiff_transitivity,
radd_comm,
radd-zero-both,
square-req-1-iff,
rless_wf,
rminus_wf,
real_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_functionElimination,
thin,
hypothesis,
isectElimination,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesisEquality,
because_Cache,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
inrFormation,
dependent_set_memberFormation,
addEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
computeAll,
minusEquality
Latex:
rsin(\mpi{}/2(slower)) = r1
Date html generated:
2016_10_26-PM-00_20_41
Last ObjectModification:
2016_09_12-PM-05_42_08
Theory : reals_2
Home
Index