Beginning of Section A304832

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.

(*** $I sig/OEISPreamble.mgs ***)

(*** Bounty 1 PFG TMLDPofWcGgNgbf5D8CBWb26uTJpZdv633D ***)

Variable F0 : set → set → set

L10

Hypothesis HF0 : ∀x0 ∈ int, ∀x1 ∈ int, F0 x0 x1 ∈ int

L11

Variable G0 : set

L12

Hypothesis HG0 : G0 ∈ int

L13

Variable H0 : set → set

L14

Hypothesis HH0 : ∀x0 ∈ int, H0 x0 ∈ int

L15

Variable I0 : set → set

L16

Hypothesis HI0 : ∀x0 ∈ int, I0 x0 ∈ int

L17

Variable J0 : set → set

L18

Hypothesis HJ0 : ∀x0 ∈ int, J0 x0 ∈ int

L19

Variable U0 : set → set → set → set

L20

Hypothesis HU0 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, U0 x0 x1 x2 ∈ int

L21

Variable V0 : set → set → set → set

L22

Hypothesis HV0 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, V0 x0 x1 x2 ∈ int

L23

Variable W0 : set → set

L24

Hypothesis HW0 : ∀x0 ∈ int, W0 x0 ∈ int

L25

Variable SMALL : set → set

L26

Hypothesis HSMALL : ∀x0 ∈ int, SMALL x0 ∈ int

L27

Variable FAST : set → set

L28

Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int

L29

Hypothesis H1 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = ((((2 * (2 + 2)) + Y) * Y) + X))))

L30

Hypothesis H2 : (G0 = 2)

L31

Hypothesis H3 : (∀X ∈ int, ((H0 X) = (2 + X)))

L32

Hypothesis H4 : (∀X ∈ int, ((I0 X) = X))

L33

Hypothesis H5 : (∀X ∈ int, ((J0 X) = X))

L34

Hypothesis H6 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((U0 X Y Z) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y Z) (V0 (X + - 1) Y Z)))))))

L35

Hypothesis H7 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((V0 X Y Z) = (if (X <= 0) then Z else G0)))))

L36

Hypothesis H8 : (∀X ∈ int, ((W0 X) = (U0 (H0 X) (I0 X) (J0 X))))

L37

Hypothesis H9 : (∀X ∈ int, ((SMALL X) = (W0 X)))

L38

Hypothesis H10 : (∀X ∈ int, ((FAST X) = (((2 * ((1 + (2 + 2)) * (2 + ((X + X) + X)))) + - X) + (X * X))))

L39

Theorem. (A304832)

(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))

In Proofgold the corresponding term root is bae28a... and proposition id is f244ef...

Proof:
Proof not loaded.