Beginning of Section A33595
Notation. We use - as a prefix operator with priority 358 corresponding to applying term minus_SNo.
Notation. We use + as an infix operator with priority 360 and which associates to the right corresponding to applying term add_SNo.
Notation. We use * as an infix operator with priority 355 and which associates to the right corresponding to applying term mul_SNo.
Notation. We use < as an infix operator with priority 490 and no associativity corresponding to applying term SNoLt.
Notation. We use <= as an infix operator with priority 490 and no associativity corresponding to applying term SNoLe.
Variable F0 : setsetset
Hypothesis HF0 : ∀x0int, ∀x1int, F0 x0 x1 int
Variable G0 : setset
Hypothesis HG0 : ∀x0int, G0 x0 int
Variable H0 : set
Hypothesis HH0 : H0 int
Variable U0 : setsetset
Hypothesis HU0 : ∀x0int, ∀x1int, U0 x0 x1 int
Variable V0 : setset
Hypothesis HV0 : ∀x0int, V0 x0 int
Variable SMALL : setset
Hypothesis HSMALL : ∀x0int, SMALL x0 int
Variable FAST : setset
Hypothesis HFAST : ∀x0int, FAST x0 int
Hypothesis H1 : (∀Xint, (∀Yint, ((F0 X Y) = ((X + - 2) + Y))))
Hypothesis H2 : (∀Xint, ((G0 X) = (2 * (X * X))))
Hypothesis H3 : (H0 = 1)
Hypothesis H4 : (∀Xint, (∀Yint, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))
Hypothesis H5 : (∀Xint, ((V0 X) = (U0 (G0 X) H0)))
Hypothesis H6 : (∀Xint, ((SMALL X) = (V0 X)))
Hypothesis H7 : (∀Xint, ((FAST X) = ((1 + - (2 * (X * X))) * (1 + - (X * X)))))
Theorem. (A33595)
(∀Nint, ((0 <= N)((SMALL N) = (FAST N))))
Proof:
The rest of the proof is missing.

End of Section A33595