Beginning of Section A123828
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 TMWVLhX7SZiKXpiittuN4mugAprrpPACBHK ***)
L9
Variable F1 : set → set
L10
Hypothesis HF1 : ∀x0 ∈ int, F1 x0 ∈ int
L11
Variable G1 : set
L12
Hypothesis HG1 : G1 ∈ int
L13
Variable H1 : set → set → set
L14
Hypothesis HH1 : ∀x0 ∈ int, ∀x1 ∈ int, H1 x0 x1 ∈ int
L15
Variable U1 : set → set → set
L16
Hypothesis HU1 : ∀x0 ∈ int, ∀x1 ∈ int, U1 x0 x1 ∈ int
L17
Variable V1 : set → set → set
L18
Hypothesis HV1 : ∀x0 ∈ int, ∀x1 ∈ int, V1 x0 x1 ∈ int
L19
Variable F0 : set → set → set
L20
Hypothesis HF0 : ∀x0 ∈ int, ∀x1 ∈ int, F0 x0 x1 ∈ int
L21
Variable G0 : set → set
L22
Hypothesis HG0 : ∀x0 ∈ int, G0 x0 ∈ int
L23
Variable H0 : set
L24
Hypothesis HH0 : H0 ∈ int
L25
Variable U0 : set → set → set
L26
Hypothesis HU0 : ∀x0 ∈ int, ∀x1 ∈ int, U0 x0 x1 ∈ int
L27
Variable V0 : set → set
L28
Hypothesis HV0 : ∀x0 ∈ int, V0 x0 ∈ int
L29
Variable SMALL : set → set
L30
Hypothesis HSMALL : ∀x0 ∈ int, SMALL x0 ∈ int
L31
Variable F2 : set → set → set
L32
Hypothesis HF2 : ∀x0 ∈ int, ∀x1 ∈ int, F2 x0 x1 ∈ int
L33
Variable G2 : set → set
L34
Hypothesis HG2 : ∀x0 ∈ int, G2 x0 ∈ int
L35
Variable H2 : set
L36
Hypothesis HH2 : H2 ∈ int
L37
Variable U2 : set → set → set
L38
Hypothesis HU2 : ∀x0 ∈ int, ∀x1 ∈ int, U2 x0 x1 ∈ int
L39
Variable V2 : set → set
L40
Hypothesis HV2 : ∀x0 ∈ int, V2 x0 ∈ int
L41
Variable FAST : set → set
L42
Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L43
Hypothesis H1 : (∀X ∈ int, ((F1 X) = (2 + (X + X))))
L44
Hypothesis H2 : (G1 = 2)
L45
Hypothesis H3 : (∀X ∈ int, (∀Y ∈ int, ((H1 X Y) = Y)))
L46
Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U1 X Y) = (if (X <= 0) then Y else (F1 (U1 (X + - 1) Y))))))
L47
Hypothesis H5 : (∀X ∈ int, (∀Y ∈ int, ((V1 X Y) = (U1 G1 (H1 X Y)))))
L48
Hypothesis H6 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = (2 * ((V1 X Y) * X)))))
L49
Hypothesis H7 : (∀X ∈ int, ((G0 X) = X))
L50
Hypothesis H8 : (H0 = 2)
L51
Hypothesis H9 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))
L52
Hypothesis H10 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) H0)))
L53
Hypothesis H11 : (∀X ∈ int, ((SMALL X) = ((V0 X) * (1 + X))))
L54
Hypothesis H12 : (∀X ∈ int, (∀Y ∈ int, ((F2 X Y) = (2 * (2 * ((2 * ((X * Y) + X)) + X))))))
L55
Hypothesis H13 : (∀X ∈ int, ((G2 X) = X))
L56
Hypothesis H14 : (H2 = 2)
L57
Hypothesis H15 : (∀X ∈ int, (∀Y ∈ int, ((U2 X Y) = (if (X <= 0) then Y else (F2 (U2 (X + - 1) Y) X)))))
L58
Hypothesis H16 : (∀X ∈ int, ((V2 X) = (U2 (G2 X) H2)))
L59
Hypothesis H17 : (∀X ∈ int, ((FAST X) = ((V2 X) * (1 + X))))
L60
Theorem. (A123828)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
In Proofgold the corresponding term root is 25a650... and proposition id is 20b45e...
Proof:
Proof not loaded.
End of Section A123828