Nuprl Lemma : rcos-rminus
∀x:ℝ. (rcos(-(x)) = rcos(x))
Proof
Definitions occuring in Statement :
rcos: rcos(x),
req: x = y,
rminus: -(x),
real: ℝ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ
Lemmas referenced :
cosine-rminus,
real_wf,
req_functionality,
rcos_wf,
rminus_wf,
cosine_wf,
rcos-is-cosine,
all_wf,
req_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
addLevel,
allFunctionality,
isectElimination,
independent_isectElimination,
productElimination,
sqequalRule,
lambdaEquality
Latex:
\mforall{}x:\mBbbR{}. (rcos(-(x)) = rcos(x))
Date html generated:
2016_10_26-PM-00_14_35
Last ObjectModification:
2016_09_12-PM-05_40_23
Theory : reals_2
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