Beginning of Section A212699
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 TMWfGzLLJSAagKgjSbdTzaUPNYmUAxVRxtV ***)
L9
Variable F0 : set → set
L10
Hypothesis HF0 : ∀x0 ∈ int, F0 x0 ∈ 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, ((F0 X) = ((2 * (X + X)) + 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))))))
L43
Hypothesis H5 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) (H0 X))))
L44
Hypothesis H6 : (∀X ∈ int, ((SMALL X) = (2 * (2 * (V0 X)))))
L45
Hypothesis H7 : (∀X ∈ int, (∀Y ∈ int, ((F1 X Y) = (X * Y))))
L46
Hypothesis H8 : (∀X ∈ int, (∀Y ∈ int, ((G1 X Y) = Y)))
L47
Hypothesis H9 : (∀X ∈ int, ((H1 X) = X))
L48
Hypothesis H10 : (∀X ∈ int, ((I1 X) = (1 + X)))
L49
Hypothesis H11 : (J1 = (1 + (2 + 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) = (2 * (2 * (W1 X)))))
L54
Theorem. (A212699)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
In Proofgold the corresponding term root is caa9c0... and proposition id is 58adf1...
Proof:
Proof not loaded.
End of Section A212699