Nuprl Lemma : rtan_wf
∀x:{x:ℝ| x ∈ (-(π/2), π/2)} . (rtan(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
rtan: rtan(x),
halfpi: π/2,
rooint: (l, u),
i-member: r ∈ I,
rminus: -(x),
real: ℝ,
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
rtan: rtan(x),
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
rcos-positive,
rdiv_wf,
rsin_wf,
rcos_wf,
rless_wf,
int-to-real_wf,
set_wf,
real_wf,
i-member_wf,
rooint_wf,
rminus_wf,
halfpi_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
setElimination,
rename,
sqequalRule,
isectElimination,
because_Cache,
independent_isectElimination,
inrFormation,
natural_numberEquality,
lambdaEquality
Latex:
\mforall{}x:\{x:\mBbbR{}| x \mmember{} (-(\mpi{}/2), \mpi{}/2)\} . (rtan(x) \mmember{} \mBbbR{})
Date html generated:
2018_05_22-PM-02_59_16
Last ObjectModification:
2017_10_19-PM-05_19_05
Theory : reals_2
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