Beginning of Section A81065
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 TMFRV2C3QhfbcosZzqNv29yUpk8pmatnc2z ***)
L9
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 I0 : set
L16
Hypothesis HI0 : I0 ∈ int
L17
Variable J0 : set
L18
Hypothesis HJ0 : J0 ∈ 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 F1 : set → set → set
L28
Hypothesis HF1 : ∀x0 ∈ int, ∀x1 ∈ int, F1 x0 x1 ∈ int
L29
Variable G1 : set → set
L30
Hypothesis HG1 : ∀x0 ∈ int, G1 x0 ∈ int
L31
Variable H1 : set → set
L32
Hypothesis HH1 : ∀x0 ∈ int, H1 x0 ∈ int
L33
Variable I1 : set
L34
Hypothesis HI1 : I1 ∈ int
L35
Variable J1 : set
L36
Hypothesis HJ1 : J1 ∈ int
L37
Variable U1 : set → set → set → set
L38
Hypothesis HU1 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, U1 x0 x1 x2 ∈ int
L39
Variable V1 : set → set → set → set
L40
Hypothesis HV1 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, V1 x0 x1 x2 ∈ int
L41
Variable W1 : set → set
L42
Hypothesis HW1 : ∀x0 ∈ int, W1 x0 ∈ int
L43
Variable F2 : set → set → set
L44
Hypothesis HF2 : ∀x0 ∈ int, ∀x1 ∈ int, F2 x0 x1 ∈ int
L45
Variable G2 : set → set
L46
Hypothesis HG2 : ∀x0 ∈ int, G2 x0 ∈ int
L47
Variable H2 : set → set
L48
Hypothesis HH2 : ∀x0 ∈ int, H2 x0 ∈ int
L49
Variable I2 : set → set
L50
Hypothesis HI2 : ∀x0 ∈ int, I2 x0 ∈ int
L51
Variable J2 : set
L52
Hypothesis HJ2 : J2 ∈ int
L53
Variable U2 : set → set → set → set
L54
Hypothesis HU2 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, U2 x0 x1 x2 ∈ int
L55
Variable V2 : set → set → set → set
L56
Hypothesis HV2 : ∀x0 ∈ int, ∀x1 ∈ int, ∀x2 ∈ int, V2 x0 x1 x2 ∈ int
L57
Variable W2 : set → set
L58
Hypothesis HW2 : ∀x0 ∈ int, W2 x0 ∈ int
L59
Variable FAST : set → set
L60
Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L61
Hypothesis H1 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = (2 + - ((2 * (X + X)) + Y)))))
L62
Hypothesis H2 : (∀X ∈ int, ((G0 X) = X))
L63
Hypothesis H3 : (∀X ∈ int, ((H0 X) = (X + X)))
L64
Hypothesis H4 : (I0 = 2)
L65
Hypothesis H5 : (J0 = 0)
L66
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)))))))
L67
Hypothesis H7 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((V0 X Y Z) = (if (X <= 0) then Z else (G0 (U0 (X + - 1) Y Z)))))))
L68
Hypothesis H8 : (∀X ∈ int, ((W0 X) = (U0 (H0 X) I0 J0)))
L69
Hypothesis H9 : (∀X ∈ int, ((SMALL X) = (W0 X)))
L70
Hypothesis H10 : (∀X ∈ int, (∀Y ∈ int, ((F1 X Y) = ((2 * (X + X)) + - Y))))
L71
Hypothesis H11 : (∀X ∈ int, ((G1 X) = X))
L72
Hypothesis H12 : (∀X ∈ int, ((H1 X) = X))
L73
Hypothesis H13 : (I1 = 2)
L74
Hypothesis H14 : (J1 = 0)
L75
Hypothesis H15 : (∀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)))))))
L76
Hypothesis H16 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((V1 X Y Z) = (if (X <= 0) then Z else (G1 (U1 (X + - 1) Y Z)))))))
L77
Hypothesis H17 : (∀X ∈ int, ((W1 X) = (U1 (H1 X) I1 J1)))
L78
Hypothesis H18 : (∀X ∈ int, (∀Y ∈ int, ((F2 X Y) = ((2 * (X + X)) + - Y))))
L79
Hypothesis H19 : (∀X ∈ int, ((G2 X) = X))
L80
Hypothesis H20 : (∀X ∈ int, ((H2 X) = (X + - 1)))
L81
Hypothesis H21 : (∀X ∈ int, ((I2 X) = ((if (X <= 0) then 0 else 2) + 1)))
L82
Hypothesis H22 : (J2 = 1)
L83
Hypothesis H23 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((U2 X Y Z) = (if (X <= 0) then Y else (F2 (U2 (X + - 1) Y Z) (V2 (X + - 1) Y Z)))))))
L84
Hypothesis H24 : (∀X ∈ int, (∀Y ∈ int, (∀Z ∈ int, ((V2 X Y Z) = (if (X <= 0) then Z else (G2 (U2 (X + - 1) Y Z)))))))
L85
Hypothesis H25 : (∀X ∈ int, ((W2 X) = (U2 (H2 X) (I2 X) J2)))
L86
Hypothesis H26 : (∀X ∈ int, ((FAST X) = ((W1 X) * (W2 X))))
L87
Theorem. (A81065)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
In Proofgold the corresponding term root is f50027... and proposition id is c72616...
Proof:
Proof not loaded.
End of Section A81065