Simply makes Plus look more pleasant.

NatWhichCanAdd n (Plus more Is nPlusMore)

You might want a function, where one N-X-Nat should be at least as big as another one.

unsafeInterval : Nat first -> Nat maybeMoreThanFirst -> Interval

We cannot promise that first Plus maybeMore Is maybeMoreThanFirst. Or can we?

type NatWhichCanAdd n addAbility
    = NatWhichCanAdd Int


oneWithAddAbility : NatWhichCanAdd N1Nat (Plus more Is (N1NatPlus more))
oneWithAddAbility =
    NatWhichCanAdd 1


add1WithAddAbility :
    NatWhichCanAdd n (Plus more Is nPlusMore)
    -> NatWhichCanAdd (N1NatPlus n) (Plus more Is (N1NatPlus nPlusMore))
add1WithAddAbility nNatWhichCanAdd =
    let
        (NatWhichCanAdd int) =
    in
    NatWhichCanAdd (int + 1)

We defined the ability to add!

safeInterval :
    NatWhichCanAdd first (Plus maybeMore Is last)
    -> NatWhichCanAdd last addAbility
    -> Interval

At least 1000.

At least 1001.

At least 1002.

At least 1003.

At least 1004.

At least 1005.

At least 1006.

At least 1007.

At least 1008.

At least 1009.

At least 100.

At least 1010.

At least 1011.

At least 1012.

At least 1013.

At least 1014.

At least 1015.

At least 1016.

At least 1017.

At least 1018.

At least 1019.

At least 101.

At least 1020.

At least 1021.

At least 1022.

At least 1023.

At least 1024.

At least 102.

At least 103.

At least 104.

At least 105.

At least 106.

At least 107.

At least 108.

At least 109.

At least 10.

At least 110.

At least 111.

At least 112.

At least 113.

At least 114.

At least 115.

At least 116.

At least 117.

At least 118.

At least 119.

At least 11.

At least 120.

At least 121.

At least 122.

At least 123.

At least 124.

At least 125.

At least 126.

At least 127.

At least 128.

At least 129.

At least 12.

At least 130.

At least 131.

At least 132.

At least 133.

At least 134.

At least 135.

At least 136.

At least 137.

At least 138.

At least 139.

At least 13.

At least 140.

At least 141.

At least 142.

At least 143.

At least 144.

At least 145.

At least 146.

At least 147.

At least 148.

At least 149.

At least 14.

At least 150.

At least 151.

At least 152.

At least 153.

At least 154.

At least 155.

At least 156.

At least 157.

At least 158.

At least 159.

At least 15.

At least 160.

At least 161.

At least 162.

At least 163.

At least 164.

At least 165.

At least 166.

At least 167.

At least 168.

At least 169.

At least 16.

At least 170.

At least 171.

At least 172.

At least 173.

At least 174.

At least 175.

At least 176.

At least 177.

At least 178.

At least 179.

At least 17.

At least 180.

At least 181.

At least 182.

At least 183.

At least 184.

At least 185.

At least 186.

At least 187.

At least 188.

At least 189.

At least 18.

At least 190.

At least 191.

At least 192.

At least 193.

At least 194.

At least 195.

At least 196.

At least 197.

At least 198.

At least 199.

At least 19.

At least 1.

At least 200.

At least 201.

At least 202.

At least 203.

At least 204.

At least 205.

At least 206.

At least 207.

At least 208.

At least 209.

At least 20.

At least 210.

At least 211.

At least 212.

At least 213.

At least 214.

At least 215.

At least 216.

At least 217.

At least 218.

At least 219.

At least 21.

At least 220.

At least 221.

At least 222.

At least 223.

At least 224.

At least 225.

At least 226.

At least 227.

At least 228.

At least 229.

At least 22.

At least 230.

At least 231.

At least 232.

At least 233.

At least 234.

At least 235.

At least 236.

At least 237.

At least 238.

At least 239.

At least 23.

At least 240.

At least 241.

At least 242.

At least 243.

At least 244.

At least 245.

At least 246.

At least 247.

At least 248.

At least 249.

At least 24.

At least 250.

At least 251.

At least 252.

At least 253.

At least 254.

At least 255.

At least 256.

At least 257.

At least 258.

At least 259.

At least 25.

At least 260.

At least 261.

At least 262.

At least 263.

At least 264.

At least 265.

At least 266.

At least 267.

At least 268.

At least 269.

At least 26.

At least 270.

At least 271.

At least 272.

At least 273.

At least 274.

At least 275.

At least 276.

At least 277.

At least 278.

At least 279.

At least 27.

At least 280.

At least 281.

At least 282.

At least 283.

At least 284.

At least 285.

At least 286.

At least 287.

At least 288.

At least 289.

At least 28.

At least 290.

At least 291.

At least 292.

At least 293.

At least 294.

At least 295.

At least 296.

At least 297.

At least 298.

At least 299.

At least 29.

At least 2.

At least 300.

At least 301.

At least 302.

At least 303.

At least 304.

At least 305.

At least 306.

At least 307.

At least 308.

At least 309.

At least 30.

At least 310.

At least 311.

At least 312.

At least 313.

At least 314.

At least 315.

At least 316.

At least 317.

At least 318.

At least 319.

At least 31.

At least 320.

At least 321.

At least 322.

At least 323.

At least 324.

At least 325.

At least 326.

At least 327.

At least 328.

At least 329.

At least 32.

At least 330.

At least 331.

At least 332.

At least 333.

At least 334.

At least 335.

At least 336.

At least 337.

At least 338.

At least 339.

At least 33.

At least 340.

At least 341.

At least 342.

At least 343.

At least 344.

At least 345.

At least 346.

At least 347.

At least 348.

At least 349.

At least 34.

At least 350.

At least 351.

At least 352.

At least 353.

At least 354.

At least 355.

At least 356.

At least 357.

At least 358.

At least 359.

At least 35.

At least 360.

At least 361.

At least 362.

At least 363.

At least 364.

At least 365.

At least 366.

At least 367.

At least 368.

At least 369.

At least 36.

At least 370.

At least 371.

At least 372.

At least 373.

At least 374.

At least 375.

At least 376.

At least 377.

At least 378.

At least 379.

At least 37.

At least 380.

At least 381.

At least 382.

At least 383.

At least 384.

At least 385.

At least 386.

At least 387.

At least 388.

At least 389.

At least 38.

At least 390.

At least 391.

At least 392.

At least 393.

At least 394.

At least 395.

At least 396.

At least 397.

At least 398.

At least 399.

At least 39.

At least 3.

At least 400.

At least 401.

At least 402.

At least 403.

At least 404.

At least 405.

At least 406.

At least 407.

At least 408.

At least 409.

At least 40.

At least 410.

At least 411.

At least 412.

At least 413.

At least 414.

At least 415.

At least 416.

At least 417.

At least 418.

At least 419.

At least 41.

At least 420.

At least 421.

At least 422.

At least 423.

At least 424.

At least 425.

At least 426.

At least 427.

At least 428.

At least 429.

At least 42.

At least 430.

At least 431.

At least 432.

At least 433.

At least 434.

At least 435.

At least 436.

At least 437.

At least 438.

At least 439.

At least 43.

At least 440.

At least 441.

At least 442.

At least 443.

At least 444.

At least 445.

At least 446.

At least 447.

At least 448.

At least 449.

At least 44.

At least 450.

At least 451.

At least 452.

At least 453.

At least 454.

At least 455.

At least 456.

At least 457.

At least 458.

At least 459.

At least 45.

At least 460.

At least 461.

At least 462.

At least 463.

At least 464.

At least 465.

At least 466.

At least 467.

At least 468.

At least 469.

At least 46.

At least 470.

At least 471.

At least 472.

At least 473.

At least 474.

At least 475.

At least 476.

At least 477.

At least 478.

At least 479.

At least 47.

At least 480.

At least 481.

At least 482.

At least 483.

At least 484.

At least 485.

At least 486.

At least 487.

At least 488.

At least 489.

At least 48.

At least 490.

At least 491.

At least 492.

At least 493.

At least 494.

At least 495.

At least 496.

At least 497.

At least 498.

At least 499.

At least 49.

At least 4.

At least 500.

At least 501.

At least 502.

At least 503.

At least 504.

At least 505.

At least 506.

At least 507.

At least 508.

At least 509.

At least 50.

At least 510.

At least 511.

At least 512.

At least 513.

At least 514.

At least 515.

At least 516.

At least 517.

At least 518.

At least 519.

At least 51.

At least 520.

At least 521.

At least 522.

At least 523.

At least 524.

At least 525.

At least 526.

At least 527.

At least 528.

At least 529.

At least 52.

At least 530.

At least 531.

At least 532.

At least 533.

At least 534.

At least 535.

At least 536.

At least 537.

At least 538.

At least 539.

At least 53.

At least 540.

At least 541.

At least 542.

At least 543.

At least 544.

At least 545.

At least 546.

At least 547.

At least 548.

At least 549.

At least 54.

At least 550.

At least 551.

At least 552.

At least 553.

At least 554.

At least 555.

At least 556.

At least 557.

At least 558.

At least 559.

At least 55.

At least 560.

At least 561.

At least 562.

At least 563.

At least 564.

At least 565.

At least 566.

At least 567.

At least 568.

At least 569.

At least 56.

At least 570.

At least 571.

At least 572.

At least 573.

At least 574.

At least 575.

At least 576.

At least 577.

At least 578.

At least 579.

At least 57.

At least 580.

At least 581.

At least 582.

At least 583.

At least 584.

At least 585.

At least 586.

At least 587.

At least 588.

At least 589.

At least 58.

At least 590.

At least 591.

At least 592.

At least 593.

At least 594.

At least 595.

At least 596.

At least 597.

At least 598.

At least 599.

At least 59.

At least 5.

At least 600.

At least 601.

At least 602.

At least 603.

At least 604.

At least 605.

At least 606.

At least 607.

At least 608.

At least 609.

At least 60.

At least 610.

At least 611.

At least 612.

At least 613.

At least 614.

At least 615.

At least 616.

At least 617.

At least 618.

At least 619.

At least 61.

At least 620.

At least 621.

At least 622.

At least 623.

At least 624.

At least 625.

At least 626.

At least 627.