---

Step * of Lemma rtan-radd-denom-positive

∀x,y:{x:ℝ| x ∈ (-(π/2), π/2)} .
  (r0 < rcos(x)) ∧ (r0 < rcos(y)) ∧ (r0 < (r1 - rtan(x) * rtan(y))) supposing x + y ∈ (-(π/2), π/2)
BY
{ (Auto
   THEN (InstLemma `rcos-positive` [⌜x + y⌝]⋅ THENA Auto)
   THEN (RWO "rcos-radd" (-1) THENA Auto)
   THEN RepUR ``rtan`` 0
   THEN nRMul ⌜rcos(x)⌝ 0⋅
   THEN nRMul ⌜rcos(y)⌝ 0⋅
   THEN Auto) }

---

Latex:

---

Latex:
\mforall{}x,y:\{x:\mBbbR{}|  x  \mmember{}  (-(\mpi{}/2),  \mpi{}/2)\}  .
    (r0  <  rcos(x))  \mwedge{}  (r0  <  rcos(y))  \mwedge{}  (r0  <  (r1  -  rtan(x)  *  rtan(y)))  supposing  x  +  y  \mmember{}  (-(\mpi{}/2),  \mpi{}/2)


By

---

Latex:
(Auto
  THEN  (InstLemma  `rcos-positive`  [\mkleeneopen{}x  +  y\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  (RWO  "rcos-radd"  (-1)  THENA  Auto)
  THEN  RepUR  ``rtan``  0
  THEN  nRMul  \mkleeneopen{}rcos(x)\mkleeneclose{}  0\mcdot{}
  THEN  nRMul  \mkleeneopen{}rcos(y)\mkleeneclose{}  0\mcdot{}
  THEN  Auto)

---

Home Index