Beginning of Section A305067
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 F1 : set → set → set
L10Hypothesis HF1 : ∀x0 ∈ int, ∀x1 ∈ int, F1 x0 x1 ∈ int
L12Hypothesis HG1 : G1 ∈ int
L14Hypothesis HH1 : H1 ∈ int
L15Variable U1 : set → set → set
L16Hypothesis HU1 : ∀x0 ∈ int, ∀x1 ∈ int, U1 x0 x1 ∈ int
L18Hypothesis HV1 : V1 ∈ int
L19Variable F0 : set → set
L20Hypothesis HF0 : ∀x0 ∈ int, F0 x0 ∈ int
L21Variable G0 : set → set
L22Hypothesis HG0 : ∀x0 ∈ int, G0 x0 ∈ int
L24Hypothesis HH0 : H0 ∈ int
L25Variable U0 : set → set → set
L26Hypothesis HU0 : ∀x0 ∈ int, ∀x1 ∈ int, U0 x0 x1 ∈ int
L27Variable V0 : set → set
L28Hypothesis HV0 : ∀x0 ∈ int, V0 x0 ∈ int
L29Variable SMALL : set → set
L30Hypothesis HSMALL : ∀x0 ∈ int, SMALL x0 ∈ int
L31Variable F2 : set → set
L32Hypothesis HF2 : ∀x0 ∈ int, F2 x0 ∈ int
L33Variable G2 : set → set
L34Hypothesis HG2 : ∀x0 ∈ int, G2 x0 ∈ int
L36Hypothesis HH2 : H2 ∈ int
L37Variable U2 : set → set → set
L38Hypothesis HU2 : ∀x0 ∈ int, ∀x1 ∈ int, U2 x0 x1 ∈ int
L39Variable V2 : set → set
L40Hypothesis HV2 : ∀x0 ∈ int, V2 x0 ∈ int
L41Variable FAST : set → set
L42Hypothesis HFAST : ∀x0 ∈ int, FAST x0 ∈ int
L43Hypothesis H1 : (∀X ∈ int, (∀Y ∈ int, ((F1 X Y) = ((X + Y) * X))))
L44Hypothesis H2 : (G1 = 2)
L45Hypothesis H3 : (H1 = 2)
L46Hypothesis H4 : (∀X ∈ int, (∀Y ∈ int, ((U1 X Y) = (if (X <= 0) then Y else (F1 (U1 (X + - 1) Y) X)))))
L47Hypothesis H5 : (V1 = (U1 G1 H1))
L48Hypothesis H6 : (∀X ∈ int, ((F0 X) = (((V1 + - 1) + X) + X)))
L49Hypothesis H7 : (∀X ∈ int, ((G0 X) = (1 + X)))
L50Hypothesis H8 : (H0 = 0)
L51Hypothesis H9 : (∀X ∈ int, (∀Y ∈ int, ((U0 X Y) = (if (X <= 0) then Y else (F0 (U0 (X + - 1) Y))))))
L52Hypothesis H10 : (∀X ∈ int, ((V0 X) = (U0 (G0 X) H0)))
L53Hypothesis H11 : (∀X ∈ int, ((SMALL X) = ((((V0 X) + - 1) + - 2) * (1 + 2))))
L54Hypothesis H12 : (∀X ∈ int, ((F2 X) = (X + X)))
L55Hypothesis H13 : (∀X ∈ int, ((G2 X) = X))
L56Hypothesis H14 : (H2 = 2)
L57Hypothesis H15 : (∀X ∈ int, (∀Y ∈ int, ((U2 X Y) = (if (X <= 0) then Y else (F2 (U2 (X + - 1) Y))))))
L58Hypothesis H16 : (∀X ∈ int, ((V2 X) = (U2 (G2 X) H2)))
L59Hypothesis H17 : (∀X ∈ int, ((FAST X) = (((((((2 * (2 * (2 * (2 + (2 + 2))))) + - 1) * ((V2 X) + - 1)) + - 2) * (1 + 2)) + - 1) + - 2)))
L60Theorem. (
A305067)
(∀N ∈ int, ((0 <= N) → ((SMALL N) = (FAST N))))
Proof: Proof not loaded.