Beginning of Section A294318
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 TMS8q9D2Y3o4mE6QBpP2i1zqDpMwsR9yas7 ***)
L9
Variable F1 : set → set → set
L10
Hypothesis HF1 : ∀x0 ∈ int, ∀x1 ∈ int, F1 x0 x1 ∈ int
L11
Variable G1 : set → set → set
L12
Hypothesis HG1 : ∀x0 ∈ int, ∀x1 ∈ int, G1 x0 x1 ∈ int
L13
Variable H1 : set → set
L14
Hypothesis HH1 : ∀x0 ∈ int, H1 x0 ∈ 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 F4 : set → set → set
L42
Hypothesis HF4 : ∀x0 ∈ int, ∀x1 ∈ int, F4 x0 x1 ∈ int
L43
Variable G4 : set → set → set
L44
Hypothesis HG4 : ∀x0 ∈ int, ∀x1 ∈ int, G4 x0 x1 ∈ int
L45
Variable H4 : set
L46
Hypothesis HH4 : H4 ∈ int
L47
Variable U4 : set → set → set
L48
Hypothesis HU4 : ∀x0 ∈ int, ∀x1 ∈ int, U4 x0 x1 ∈ int
L49
Variable V4 : set → set → set
L50
Hypothesis HV4 : ∀x0 ∈ int, ∀x1 ∈ int, V4 x0 x1 ∈ int
L51
Variable F3 : set → set → set
L52
Hypothesis HF3 : ∀x0 ∈ int, ∀x1 ∈ int, F3 x0 x1 ∈ int
L53
Variable G3 : set → set
L54
Hypothesis HG3 : ∀x0 ∈ int, G3 x0 ∈ int
L55
Variable H3 : set
L56
Hypothesis HH3 : H3 ∈ int
L57
Variable U3 : set → set → set
L58
Hypothesis HU3 : ∀x0 ∈ int, ∀x1 ∈ int, U3 x0 x1 ∈ int
L59
Variable V3 : set → set
L60
Hypothesis HV3 : ∀x0 ∈ int, V3 x0 ∈ int
L61
Variable FAST : set → set
L62
Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L63
Hypothesis H1 : (∀X ∈ int, (∀Y ∈ int, ((F1 X Y) = ((X * Y) + X))))
L64
Hypothesis H2 : (∀X ∈ int, (∀Y ∈ int, ((G1 X Y) = ((Y + Y) + Y))))
L65
Hypothesis H3 : (∀X ∈ int, ((H1 X) = X))
L66
Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U1 X Y) = (if (X <= 0) then Y else (F1 (U1 (X + - 1) Y) X)))))
L67
Hypothesis H5 : (∀X ∈ int, (∀Y ∈ int, ((V1 X Y) = (U1 (G1 X Y) (H1 X)))))
L68
Hypothesis H6 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = (V1 X Y))))
L69
Hypothesis H7 : (∀X ∈ int, ((G0 X) = X))
L70
Hypothesis H8 : (H0 = 1)
L71
Hypothesis H9 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))
L72
Hypothesis H10 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) H0)))
L73
Hypothesis H11 : (∀X ∈ int, ((SMALL X) = (V0 X)))
L74
Hypothesis H12 : (∀X ∈ int, (∀Y ∈ int, ((F2 X Y) = (((1 + 2) * (X * Y)) + X))))
L75
Hypothesis H13 : (∀X ∈ int, ((G2 X) = X))
L76
Hypothesis H14 : (H2 = 1)
L77
Hypothesis H15 : (∀X ∈ int, (∀Y ∈ int, ((U2 X Y) = (if (X <= 0) then Y else (F2 (U2 (X + - 1) Y) X)))))
L78
Hypothesis H16 : (∀X ∈ int, ((V2 X) = (U2 (G2 X) H2)))
L79
Hypothesis H17 : (∀X ∈ int, (∀Y ∈ int, ((F4 X Y) = (X * Y))))
L80
Hypothesis H18 : (∀X ∈ int, (∀Y ∈ int, ((G4 X Y) = ((Y + Y) + Y))))
L81
Hypothesis H19 : (H4 = 1)
L82
Hypothesis H20 : (∀X ∈ int, (∀Y ∈ int, ((U4 X Y) = (if (X <= 0) then Y else (F4 (U4 (X + - 1) Y) X)))))
L83
Hypothesis H21 : (∀X ∈ int, (∀Y ∈ int, ((V4 X Y) = (U4 (G4 X Y) H4))))
L84
Hypothesis H22 : (∀X ∈ int, (∀Y ∈ int, ((F3 X Y) = ((V4 X Y) * X))))
L85
Hypothesis H23 : (∀X ∈ int, ((G3 X) = X))
L86
Hypothesis H24 : (H3 = 1)
L87
Hypothesis H25 : (∀X ∈ int, (∀Y ∈ int, ((U3 X Y) = (if (X <= 0) then Y else (F3 (U3 (X + - 1) Y) X)))))
L88
Hypothesis H26 : (∀X ∈ int, ((V3 X) = (U3 (G3 X) H3)))
L89
Hypothesis H27 : (∀X ∈ int, ((FAST X) = ((V2 X) * (V3 X))))
L90
Theorem. (A294318)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
In Proofgold the corresponding term root is 7b1ad1... and proposition id is 1eb32a...
Proof:
Proof not loaded.
End of Section A294318