SUBSET_HALFSPACES_IMP_COLLINEAR
|- ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%388. (?x. (((SETSPEC GEN%PVAR%388) ((real_lt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%389. (?x. (((SETSPEC GEN%PVAR%389) ((real_lt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%390. (?x. (((SETSPEC GEN%PVAR%390) ((real_lt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%391. (?x. (((SETSPEC GEN%PVAR%391) ((real_le ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%392. (?x. (((SETSPEC GEN%PVAR%392) ((real_lt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%393. (?x. (((SETSPEC GEN%PVAR%393) (((dot b) x) = d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%394. (?x. (((SETSPEC GEN%PVAR%394) ((real_lt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%395. (?x. (((SETSPEC GEN%PVAR%395) ((real_ge ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%396. (?x. (((SETSPEC GEN%PVAR%396) ((real_lt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%397. (?x. (((SETSPEC GEN%PVAR%397) ((real_gt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%398. (?x. (((SETSPEC GEN%PVAR%398) ((real_le ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%399. (?x. (((SETSPEC GEN%PVAR%399) ((real_lt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%400. (?x. (((SETSPEC GEN%PVAR%400) ((real_le ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%401. (?x. (((SETSPEC GEN%PVAR%401) ((real_le ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%402. (?x. (((SETSPEC GEN%PVAR%402) ((real_le ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%403. (?x. (((SETSPEC GEN%PVAR%403) (((dot b) x) = d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%404. (?x. (((SETSPEC GEN%PVAR%404) ((real_le ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%405. (?x. (((SETSPEC GEN%PVAR%405) ((real_ge ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%406. (?x. (((SETSPEC GEN%PVAR%406) ((real_le ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%407. (?x. (((SETSPEC GEN%PVAR%407) ((real_gt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%408. (?x. (((SETSPEC GEN%PVAR%408) (((dot a) x) = c)) x)))) SUBSET (GSPEC (\GEN%PVAR%409. (?x. (((SETSPEC GEN%PVAR%409) ((real_lt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%410. (?x. (((SETSPEC GEN%PVAR%410) (((dot a) x) = c)) x)))) SUBSET (GSPEC (\GEN%PVAR%411. (?x. (((SETSPEC GEN%PVAR%411) ((real_le ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%412. (?x. (((SETSPEC GEN%PVAR%412) (((dot a) x) = c)) x)))) SUBSET (GSPEC (\GEN%PVAR%413. (?x. (((SETSPEC GEN%PVAR%413) (((dot b) x) = d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%414. (?x. (((SETSPEC GEN%PVAR%414) (((dot a) x) = c)) x)))) SUBSET (GSPEC (\GEN%PVAR%415. (?x. (((SETSPEC GEN%PVAR%415) ((real_ge ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%416. (?x. (((SETSPEC GEN%PVAR%416) (((dot a) x) = c)) x)))) SUBSET (GSPEC (\GEN%PVAR%417. (?x. (((SETSPEC GEN%PVAR%417) ((real_gt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%418. (?x. (((SETSPEC GEN%PVAR%418) ((real_ge ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%419. (?x. (((SETSPEC GEN%PVAR%419) ((real_lt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%420. (?x. (((SETSPEC GEN%PVAR%420) ((real_ge ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%421. (?x. (((SETSPEC GEN%PVAR%421) ((real_le ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%422. (?x. (((SETSPEC GEN%PVAR%422) ((real_ge ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%423. (?x. (((SETSPEC GEN%PVAR%423) (((dot b) x) = d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%424. (?x. (((SETSPEC GEN%PVAR%424) ((real_ge ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%425. (?x. (((SETSPEC GEN%PVAR%425) ((real_ge ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%426. (?x. (((SETSPEC GEN%PVAR%426) ((real_ge ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%427. (?x. (((SETSPEC GEN%PVAR%427) ((real_gt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%428. (?x. (((SETSPEC GEN%PVAR%428) ((real_gt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%429. (?x. (((SETSPEC GEN%PVAR%429) ((real_lt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%430. (?x. (((SETSPEC GEN%PVAR%430) ((real_gt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%431. (?x. (((SETSPEC GEN%PVAR%431) ((real_le ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%432. (?x. (((SETSPEC GEN%PVAR%432) ((real_gt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%433. (?x. (((SETSPEC GEN%PVAR%433) (((dot b) x) = d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ ((!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%434. (?x. (((SETSPEC GEN%PVAR%434) ((real_gt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%435. (?x. (((SETSPEC GEN%PVAR%435) ((real_ge ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY))))))))) /\ (!a. (!b. (!c. (!d. (((GSPEC (\GEN%PVAR%436. (?x. (((SETSPEC GEN%PVAR%436) ((real_gt ((dot a) x)) c)) x)))) SUBSET (GSPEC (\GEN%PVAR%437. (?x. (((SETSPEC GEN%PVAR%437) ((real_gt ((dot b) x)) d)) x))))) ==> (collinear ((vec (NUMERAL _0)) INSERT (a INSERT (b INSERT EMPTY)))))))))))))))))))))))))))))))))