---

Step * 1 1 1 of Lemma rsin-pi-over-4


1. r0 = (rcos((π/r(4)))^2 - rsin((π/r(4)))^2)
2. rcos((π/r(4)) + (π/r(4))) = rcos(π/2)
3. (rsin((π/r(4)))^2 + rcos((π/r(4)))^2) = r1
⊢ rsin((π/r(4))) = (r1/rsqrt(r(2)))
BY
{ (Assert rcos((π/r(4)))^2 = rsin((π/r(4)))^2 BY
         (nRAdd ⌜rsin((π/r(4)))^2⌝ 1⋅ THEN Auto)) }

1
1. r0 = (rcos((π/r(4)))^2 - rsin((π/r(4)))^2)
2. rcos((π/r(4)) + (π/r(4))) = rcos(π/2)
3. (rsin((π/r(4)))^2 + rcos((π/r(4)))^2) = r1
4. rcos((π/r(4)))^2 = rsin((π/r(4)))^2
⊢ rsin((π/r(4))) = (r1/rsqrt(r(2)))

---

Latex:

---

Latex:

1.  r0  =  (rcos((\mpi{}/r(4)))\^{}2  -  rsin((\mpi{}/r(4)))\^{}2)
2.  rcos((\mpi{}/r(4))  +  (\mpi{}/r(4)))  =  rcos(\mpi{}/2)
3.  (rsin((\mpi{}/r(4)))\^{}2  +  rcos((\mpi{}/r(4)))\^{}2)  =  r1
\mvdash{}  rsin((\mpi{}/r(4)))  =  (r1/rsqrt(r(2)))


By

---

Latex:
(Assert  rcos((\mpi{}/r(4)))\^{}2  =  rsin((\mpi{}/r(4)))\^{}2  BY
              (nRAdd  \mkleeneopen{}rsin((\mpi{}/r(4)))\^{}2\mkleeneclose{}  1\mcdot{}  THEN  Auto))

---

Home Index