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Step * 1 of Lemma arcsin-unique


1. x : {x:ℝ| x ∈ [r(-1), r1]} 
2. y : {y:ℝ| y ∈ [-(π/2), π/2]} 
3. rsin(y) = x
4. rsin(arcsin(x)) = x
⊢ arcsin(x) = y
BY
{ InstLemma `rsin-strictly-increasing2` [] }

1
1. x : {x:ℝ| x ∈ [r(-1), r1]} 
2. y : {y:ℝ| y ∈ [-(π/2), π/2]} 
3. rsin(y) = x
4. rsin(arcsin(x)) = x
5. rsin(x) strictly-increasing for x ∈ [-(π/2), π/2]
⊢ arcsin(x) = y

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Latex:

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Latex:

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


By

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Latex:
InstLemma  `rsin-strictly-increasing2`  []

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