Beginning of Section A133073
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.
L9Variable F0 : set → set → set
L10Hypothesis HF0 : ∀x0 ∈ int, ∀x1 ∈ int, F0 x0 x1 ∈ int
L11Variable G0 : set → set
L12Hypothesis HG0 : ∀x0 ∈ int, G0 x0 ∈ int
L13Variable H0 : set → set
L14Hypothesis HH0 : ∀x0 ∈ int, H0 x0 ∈ int
L15Variable U0 : set → set → set
L16Hypothesis HU0 : ∀x0 ∈ int, ∀x1 ∈ int, U0 x0 x1 ∈ int
L17Variable V0 : set → set
L18Hypothesis HV0 : ∀x0 ∈ int, V0 x0 ∈ int
L19Variable SMALL : set → set
L20Hypothesis HSMALL : ∀x0 ∈ int, SMALL x0 ∈ int
L21Variable FAST : set → set
L22Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L23Hypothesis H1 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = ((X + Y) + Y))))
L24Hypothesis H2 : (∀X ∈ int, ((G0 X) = (X * X)))
L25Hypothesis H3 : (∀X ∈ int, ((H0 X) = X))
L26Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))
L27Hypothesis H5 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) (H0 X))))
L28Hypothesis H6 : (∀X ∈ int, ((SMALL X) = ((V0 X) * X)))
L29Hypothesis H7 : (∀X ∈ int, ((FAST X) = ((1 + (((X * X) * X) + X)) * (X * X))))
L30Theorem. (
A133073)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
Proof: Proof not loaded.