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Step * 2 1 of Lemma arcsine-bounds


1. x : {x:ℝ| x ∈ (r(-1), r1)} 
2. y : ℝ
3. y ∈ (-(π/2), π/2)
4. x = rsin(y)
⊢ arcsine(x) ∈ (-(π/2), π/2)
BY
{ (InstLemma `rsin-strict-bound` [⌜y⌝]⋅ THENA Auto) }

1
1. x : {x:ℝ| x ∈ (r(-1), r1)} 
2. y : ℝ
3. y ∈ (-(π/2), π/2)
4. x = rsin(y)
5. rsin(y) ∈ (r(-1), r1)
⊢ arcsine(x) ∈ (-(π/2), π/2)

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Latex:

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Latex:

1.  x  :  \{x:\mBbbR{}|  x  \mmember{}  (r(-1),  r1)\} 
2.  y  :  \mBbbR{}
3.  y  \mmember{}  (-(\mpi{}/2),  \mpi{}/2)
4.  x  =  rsin(y)
\mvdash{}  arcsine(x)  \mmember{}  (-(\mpi{}/2),  \mpi{}/2)


By

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Latex:
(InstLemma  `rsin-strict-bound`  [\mkleeneopen{}y\mkleeneclose{}]\mcdot{}  THENA  Auto)

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