Beginning of Section A257449
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.
L9Variable F2 : set → set
L10Hypothesis HF2 : ∀x0 ∈ int, F2 x0 ∈ int
L12Hypothesis HG2 : G2 ∈ int
L13Variable H2 : set → set
L14Hypothesis HH2 : ∀x0 ∈ int, H2 x0 ∈ int
L15Variable U2 : set → set → set
L16Hypothesis HU2 : ∀x0 ∈ int, ∀x1 ∈ int, U2 x0 x1 ∈ int
L17Variable V2 : set → set
L18Hypothesis HV2 : ∀x0 ∈ int, V2 x0 ∈ int
L19Variable F3 : set → set
L20Hypothesis HF3 : ∀x0 ∈ int, F3 x0 ∈ int
L22Hypothesis HG3 : G3 ∈ int
L23Variable H3 : set → set
L24Hypothesis HH3 : ∀x0 ∈ int, H3 x0 ∈ int
L25Variable U3 : set → set → set
L26Hypothesis HU3 : ∀x0 ∈ int, ∀x1 ∈ int, U3 x0 x1 ∈ int
L27Variable V3 : set → set
L28Hypothesis HV3 : ∀x0 ∈ int, V3 x0 ∈ int
L29Variable F1 : set → set
L30Hypothesis HF1 : ∀x0 ∈ int, F1 x0 ∈ int
L32Hypothesis HG1 : G1 ∈ int
L33Variable H1 : set → set → set
L34Hypothesis HH1 : ∀x0 ∈ int, ∀x1 ∈ int, H1 x0 x1 ∈ int
L35Variable U1 : set → set → set
L36Hypothesis HU1 : ∀x0 ∈ int, ∀x1 ∈ int, U1 x0 x1 ∈ int
L37Variable V1 : set → set → set
L38Hypothesis HV1 : ∀x0 ∈ int, ∀x1 ∈ int, V1 x0 x1 ∈ int
L39Variable F0 : set → set → set
L40Hypothesis HF0 : ∀x0 ∈ int, ∀x1 ∈ int, F0 x0 x1 ∈ int
L41Variable G0 : set → set
L42Hypothesis HG0 : ∀x0 ∈ int, G0 x0 ∈ int
L44Hypothesis HH0 : H0 ∈ int
L45Variable U0 : set → set → set
L46Hypothesis HU0 : ∀x0 ∈ int, ∀x1 ∈ int, U0 x0 x1 ∈ int
L47Variable V0 : set → set
L48Hypothesis HV0 : ∀x0 ∈ int, V0 x0 ∈ int
L49Variable SMALL : set → set
L50Hypothesis HSMALL : ∀x0 ∈ int, SMALL x0 ∈ int
L51Variable F5 : set → set
L52Hypothesis HF5 : ∀x0 ∈ int, F5 x0 ∈ int
L54Hypothesis HG5 : G5 ∈ int
L55Variable H5 : set → set → set
L56Hypothesis HH5 : ∀x0 ∈ int, ∀x1 ∈ int, H5 x0 x1 ∈ int
L57Variable U5 : set → set → set
L58Hypothesis HU5 : ∀x0 ∈ int, ∀x1 ∈ int, U5 x0 x1 ∈ int
L59Variable V5 : set → set → set
L60Hypothesis HV5 : ∀x0 ∈ int, ∀x1 ∈ int, V5 x0 x1 ∈ int
L61Variable F4 : set → set → set
L62Hypothesis HF4 : ∀x0 ∈ int, ∀x1 ∈ int, F4 x0 x1 ∈ int
L63Variable G4 : set → set
L64Hypothesis HG4 : ∀x0 ∈ int, G4 x0 ∈ int
L66Hypothesis HH4 : H4 ∈ int
L67Variable U4 : set → set → set
L68Hypothesis HU4 : ∀x0 ∈ int, ∀x1 ∈ int, U4 x0 x1 ∈ int
L69Variable V4 : set → set
L70Hypothesis HV4 : ∀x0 ∈ int, V4 x0 ∈ int
L71Variable FAST : set → set
L72Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L73Hypothesis H1 : (∀X ∈ int, ((F2 X) = (X * X)))
L74Hypothesis H2 : (G2 = 2)
L75Hypothesis H3 : (∀X ∈ int, ((H2 X) = (1 + X)))
L76Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U2 X Y) = (if (X <= 0) then Y else (F2 (U2 (X + - 1) Y))))))
L77Hypothesis H5 : (∀X ∈ int, ((V2 X) = (U2 G2 (H2 X))))
L78Hypothesis H6 : (∀X ∈ int, ((F3 X) = (X * X)))
L79Hypothesis H7 : (G3 = 2)
L80Hypothesis H8 : (∀X ∈ int, ((H3 X) = X))
L81Hypothesis H9 : (∀X ∈ int, (∀Y ∈ int, ((U3 X Y) = (if (X <= 0) then Y else (F3 (U3 (X + - 1) Y))))))
L82Hypothesis H10 : (∀X ∈ int, ((V3 X) = (U3 G3 (H3 X))))
L83Hypothesis H11 : (∀X ∈ int, ((F1 X) = ((V2 X) + - (V3 X))))
L84Hypothesis H12 : (G1 = 1)
L85Hypothesis H13 : (∀X ∈ int, (∀Y ∈ int, ((H1 X Y) = Y)))
L86Hypothesis H14 : (∀X ∈ int, (∀Y ∈ int, ((U1 X Y) = (if (X <= 0) then Y else (F1 (U1 (X + - 1) Y))))))
L87Hypothesis H15 : (∀X ∈ int, (∀Y ∈ int, ((V1 X Y) = (U1 G1 (H1 X Y)))))
L88Hypothesis H16 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = (((V1 X Y) + X) + X))))
L89Hypothesis H17 : (∀X ∈ int, ((G0 X) = X))
L90Hypothesis H18 : (H0 = 1)
L91Hypothesis H19 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))
L92Hypothesis H20 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) H0)))
L93Hypothesis H21 : (∀X ∈ int, ((SMALL X) = (V0 X)))
L94Hypothesis H22 : (∀X ∈ int, ((F5 X) = ((1 + (X + X)) * (1 + (2 * ((X * X) + X))))))
L95Hypothesis H23 : (G5 = 1)
L96Hypothesis H24 : (∀X ∈ int, (∀Y ∈ int, ((H5 X Y) = Y)))
L97Hypothesis H25 : (∀X ∈ int, (∀Y ∈ int, ((U5 X Y) = (if (X <= 0) then Y else (F5 (U5 (X + - 1) Y))))))
L98Hypothesis H26 : (∀X ∈ int, (∀Y ∈ int, ((V5 X Y) = (U5 G5 (H5 X Y)))))
L99Hypothesis H27 : (∀X ∈ int, (∀Y ∈ int, ((F4 X Y) = (((V5 X Y) + X) + X))))
L100Hypothesis H28 : (∀X ∈ int, ((G4 X) = X))
L101Hypothesis H29 : (H4 = 1)
L102Hypothesis H30 : (∀X ∈ int, (∀Y ∈ int, ((U4 X Y) = (if (X <= 0) then Y else (F4 (U4 (X + - 1) Y) X)))))
L103Hypothesis H31 : (∀X ∈ int, ((V4 X) = (U4 (G4 X) H4)))
L104Hypothesis H32 : (∀X ∈ int, ((FAST X) = (V4 X)))
L105Theorem. (
A257449)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
Proof: Proof not loaded.