Beginning of Section A204245
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 F0 : set → set → set
L10Hypothesis HF0 : ∀x0 ∈ int, ∀x1 ∈ int, F0 x0 x1 ∈ int
L11Variable G0 : set → set
L12Hypothesis HG0 : ∀x0 ∈ int, G0 x0 ∈ int
L14Hypothesis HH0 : H0 ∈ int
L15Variable U0 : set → set → set
L16Hypothesis HU0 : ∀x0 ∈ int, ∀x1 ∈ int, U0 x0 x1 ∈ int
L17Variable V0 : set → set
L18Hypothesis HV0 : ∀x0 ∈ int, V0 x0 ∈ int
L19Variable F2 : set → set → set
L20Hypothesis HF2 : ∀x0 ∈ int, ∀x1 ∈ int, F2 x0 x1 ∈ int
L21Variable G2 : set → set → set
L22Hypothesis HG2 : ∀x0 ∈ int, ∀x1 ∈ int, G2 x0 x1 ∈ int
L23Variable H2 : set → set
L24Hypothesis HH2 : ∀x0 ∈ int, H2 x0 ∈ int
L25Variable U2 : set → set → set
L26Hypothesis HU2 : ∀x0 ∈ int, ∀x1 ∈ int, U2 x0 x1 ∈ int
L27Variable V2 : set → set → set
L28Hypothesis HV2 : ∀x0 ∈ int, ∀x1 ∈ int, V2 x0 x1 ∈ int
L29Variable F1 : set → set → set
L30Hypothesis HF1 : ∀x0 ∈ int, ∀x1 ∈ int, F1 x0 x1 ∈ int
L31Variable G1 : set → set
L32Hypothesis HG1 : ∀x0 ∈ int, G1 x0 ∈ int
L34Hypothesis HH1 : H1 ∈ int
L35Variable U1 : set → set → set
L36Hypothesis HU1 : ∀x0 ∈ int, ∀x1 ∈ int, U1 x0 x1 ∈ int
L37Variable V1 : set → set
L38Hypothesis HV1 : ∀x0 ∈ int, V1 x0 ∈ int
L39Variable SMALL : set → set
L40Hypothesis HSMALL : ∀x0 ∈ int, SMALL x0 ∈ int
L41Variable F4 : set → set → set
L42Hypothesis HF4 : ∀x0 ∈ int, ∀x1 ∈ int, F4 x0 x1 ∈ int
L43Variable G4 : set → set → set
L44Hypothesis HG4 : ∀x0 ∈ int, ∀x1 ∈ int, G4 x0 x1 ∈ int
L46Hypothesis HH4 : H4 ∈ int
L47Variable U4 : set → set → set
L48Hypothesis HU4 : ∀x0 ∈ int, ∀x1 ∈ int, U4 x0 x1 ∈ int
L49Variable V4 : set → set → set
L50Hypothesis HV4 : ∀x0 ∈ int, ∀x1 ∈ int, V4 x0 x1 ∈ int
L51Variable F3 : set → set → set
L52Hypothesis HF3 : ∀x0 ∈ int, ∀x1 ∈ int, F3 x0 x1 ∈ int
L53Variable G3 : set → set
L54Hypothesis HG3 : ∀x0 ∈ int, G3 x0 ∈ int
L56Hypothesis HH3 : H3 ∈ int
L57Variable U3 : set → set → set
L58Hypothesis HU3 : ∀x0 ∈ int, ∀x1 ∈ int, U3 x0 x1 ∈ int
L59Variable V3 : set → set
L60Hypothesis HV3 : ∀x0 ∈ int, V3 x0 ∈ int
L61Variable F5 : set → set → set
L62Hypothesis HF5 : ∀x0 ∈ int, ∀x1 ∈ int, F5 x0 x1 ∈ int
L63Variable G5 : set → set
L64Hypothesis HG5 : ∀x0 ∈ int, G5 x0 ∈ int
L66Hypothesis HH5 : H5 ∈ int
L67Variable U5 : set → set → set
L68Hypothesis HU5 : ∀x0 ∈ int, ∀x1 ∈ int, U5 x0 x1 ∈ int
L69Variable V5 : set → set
L70Hypothesis HV5 : ∀x0 ∈ int, V5 x0 ∈ int
L71Variable F6 : set → set → set
L72Hypothesis HF6 : ∀x0 ∈ int, ∀x1 ∈ int, F6 x0 x1 ∈ int
L73Variable G6 : set → set
L74Hypothesis HG6 : ∀x0 ∈ int, G6 x0 ∈ int
L76Hypothesis HH6 : H6 ∈ int
L77Variable U6 : set → set → set
L78Hypothesis HU6 : ∀x0 ∈ int, ∀x1 ∈ int, U6 x0 x1 ∈ int
L79Variable V6 : set → set
L80Hypothesis HV6 : ∀x0 ∈ int, V6 x0 ∈ int
L81Variable FAST : set → set
L82Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L83Hypothesis H1 : (∀X ∈ int, (∀Y ∈ int, ((F0 X Y) = (((X * Y) + - 1) + X))))
L84Hypothesis H2 : (∀X ∈ int, ((G0 X) = X))
L85Hypothesis H3 : (H0 = 1)
L86Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y) X)))))
L87Hypothesis H5 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) H0)))
L88Hypothesis H6 : (∀X ∈ int, (∀Y ∈ int, ((F2 X Y) = (X * Y))))
L89Hypothesis H7 : (∀X ∈ int, (∀Y ∈ int, ((G2 X Y) = Y)))
L90Hypothesis H8 : (∀X ∈ int, ((H2 X) = X))
L91Hypothesis H9 : (∀X ∈ int, (∀Y ∈ int, ((U2 X Y) = (if (X <= 0) then Y else (F2 (U2 (X + - 1) Y) X)))))
L92Hypothesis H10 : (∀X ∈ int, (∀Y ∈ int, ((V2 X Y) = (U2 (G2 X Y) (H2 X)))))
L93Hypothesis H11 : (∀X ∈ int, (∀Y ∈ int, ((F1 X Y) = (V2 X Y))))
L94Hypothesis H12 : (∀X ∈ int, ((G1 X) = X))
L95Hypothesis H13 : (H1 = 1)
L96Hypothesis H14 : (∀X ∈ int, (∀Y ∈ int, ((U1 X Y) = (if (X <= 0) then Y else (F1 (U1 (X + - 1) Y) X)))))
L97Hypothesis H15 : (∀X ∈ int, ((V1 X) = (U1 (G1 X) H1)))
L98Hypothesis H16 : (∀X ∈ int, ((SMALL X) = ((V0 X) * (V1 X))))
L99Hypothesis H17 : (∀X ∈ int, (∀Y ∈ int, ((F4 X Y) = (X * Y))))
L100Hypothesis H18 : (∀X ∈ int, (∀Y ∈ int, ((G4 X Y) = Y)))
L101Hypothesis H19 : (H4 = 1)
L102Hypothesis H20 : (∀X ∈ int, (∀Y ∈ int, ((U4 X Y) = (if (X <= 0) then Y else (F4 (U4 (X + - 1) Y) X)))))
L103Hypothesis H21 : (∀X ∈ int, (∀Y ∈ int, ((V4 X Y) = (U4 (G4 X Y) H4))))
L104Hypothesis H22 : (∀X ∈ int, (∀Y ∈ int, ((F3 X Y) = ((V4 X Y) * X))))
L105Hypothesis H23 : (∀X ∈ int, ((G3 X) = (X + - 1)))
L106Hypothesis H24 : (H3 = 1)
L107Hypothesis H25 : (∀X ∈ int, (∀Y ∈ int, ((U3 X Y) = (if (X <= 0) then Y else (F3 (U3 (X + - 1) Y) X)))))
L108Hypothesis H26 : (∀X ∈ int, ((V3 X) = (U3 (G3 X) H3)))
L109Hypothesis H27 : (∀X ∈ int, (∀Y ∈ int, ((F5 X Y) = (X * Y))))
L110Hypothesis H28 : (∀X ∈ int, ((G5 X) = X))
L111Hypothesis H29 : (H5 = 1)
L112Hypothesis H30 : (∀X ∈ int, (∀Y ∈ int, ((U5 X Y) = (if (X <= 0) then Y else (F5 (U5 (X + - 1) Y) X)))))
L113Hypothesis H31 : (∀X ∈ int, ((V5 X) = (U5 (G5 X) H5)))
L114Hypothesis H32 : (∀X ∈ int, (∀Y ∈ int, ((F6 X Y) = ((X * Y) + (X + - 1)))))
L115Hypothesis H33 : (∀X ∈ int, ((G6 X) = X))
L116Hypothesis H34 : (H6 = 1)
L117Hypothesis H35 : (∀X ∈ int, (∀Y ∈ int, ((U6 X Y) = (if (X <= 0) then Y else (F6 (U6 (X + - 1) Y) X)))))
L118Hypothesis H36 : (∀X ∈ int, ((V6 X) = (U6 (G6 X) H6)))
L119Hypothesis H37 : (∀X ∈ int, ((FAST X) = (((V3 X) * (V5 X)) * (V6 X))))
L120Theorem. (
A204245)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
Proof: Proof not loaded.