Nuprl Lemma : rsin-rminus
∀x:ℝ. (rsin(-(x)) = -(rsin(x)))
Proof
Definitions occuring in Statement :
rsin: rsin(x),
req: x = y,
rminus: -(x),
real: ℝ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
rfun: I ⟶ℝ,
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
rfun-eq: rfun-eq(I;f;g),
r-ap: f(x),
top: Top,
true: True,
guard: {T}
Lemmas referenced :
derivative_unique,
riiint_wf,
iproper-riiint,
rcos_wf,
real_wf,
i-member_wf,
rminus_wf,
rsin_wf,
deriviative-rcos,
simple-chain-rule,
derivative-function-rminus,
req_wf,
req_weakening,
req_functionality,
rminus_functionality,
rsin_functionality,
set_wf,
rminus-rminus,
derivative_functionality,
member_riiint_lemma,
rcos-rminus,
true_wf,
req_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_functionElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
setEquality,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
natural_numberEquality
Latex:
\mforall{}x:\mBbbR{}. (rsin(-(x)) = -(rsin(x)))
Date html generated:
2016_10_26-PM-00_14_54
Last ObjectModification:
2016_09_12-PM-05_40_37
Theory : reals_2
Home
Index