Beginning of Section A1879

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 TMPP82D79NREWh8HwK1i15WHLuwqKgvwGy1 ***)

Variable F0 : set → set → set

L10

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

L11

Variable G0 : set → set

L12

Hypothesis HG0 : ∀x0 ∈ int, G0 x0 ∈ int

L13

Variable H0 : set → set

L14

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

L15

Variable U0 : set → set → set

L16

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

L17

Variable V0 : set → set

L18

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

L19

Variable SMALL : set → set

L20

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

L21

Variable F1 : set → set → set

L22

Hypothesis HF1 : ∀x0 ∈ int, ∀x1 ∈ int, F1 x0 x1 ∈ int

L23

Variable G1 : set → set → set

L24

Hypothesis HG1 : ∀x0 ∈ int, ∀x1 ∈ int, G1 x0 x1 ∈ int

L25

Variable H1 : set → set

L26

Hypothesis HH1 : ∀x0 ∈ int, H1 x0 ∈ int

L27

Variable I1 : set → set

L28

Hypothesis HI1 : ∀x0 ∈ int, I1 x0 ∈ int

L29

Variable J1 : set

L30

Hypothesis HJ1 : J1 ∈ int

L31

Variable U1 : set → set → set → set

L32

Hypothesis HU1 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, U1 x0 x1 x2 ∈ int

L33

Variable V1 : set → set → set → set

L34

Hypothesis HV1 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, V1 x0 x1 x2 ∈ int

L35

Variable W1 : set → set

L36

Hypothesis HW1 : ∀x0 ∈ int, W1 x0 ∈ int

L37

Variable FAST : set → set

L38

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

L39

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

L40

Hypothesis H2 : (∀X ∈ int, ((G0 X) = X))

L41

Hypothesis H3 : (∀X ∈ int, ((H0 X) = (1 + X)))

L42

Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))

L43

Hypothesis H5 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) (H0 X))))

L44

Hypothesis H6 : (∀X ∈ int, ((SMALL X) = (V0 X)))

L45

Hypothesis H7 : (∀X ∈ int, (∀Y ∈ int, ((F1 X Y) = (X * Y))))

L46

Hypothesis H8 : (∀X ∈ int, (∀Y ∈ int, ((G1 X Y) = (2 + Y))))

L47

Hypothesis H9 : (∀X ∈ int, ((H1 X) = (X + - 1)))

L48

Hypothesis H10 : (∀X ∈ int, ((I1 X) = (1 + X)))

L49

Hypothesis H11 : (J1 = (1 + 2))

L50

Hypothesis H12 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((U1 X Y Z) = (if (X <= 0) then Y else (F1 (U1 (X + - 1) Y Z) (V1 (X + - 1) Y Z)))))))

L51

Hypothesis H13 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((V1 X Y Z) = (if (X <= 0) then Z else (G1 (U1 (X + - 1) Y Z) (V1 (X + - 1) Y Z)))))))

L52

Hypothesis H14 : (∀X ∈ int, ((W1 X) = (U1 (H1 X) (I1 X) J1)))

L53

Hypothesis H15 : (∀X ∈ int, ((FAST X) = ((1 + (X + X)) * (W1 X))))

L54

Theorem. (A1879)

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

In Proofgold the corresponding term root is d9e40f... and proposition id is cdcd87...

Proof:
Proof not loaded.