2014-09-15 17:25:07 +00:00
|
|
|
-- BEGINWAIT
|
|
|
|
|
-- ENDWAIT
|
|
|
|
|
-- BEGINSET
|
|
|
|
|
-- ENDSET
|
|
|
|
|
-- BEGINFINDP
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.size|pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.bit0|pos_num → pos_num
|
|
|
|
|
pos_num.is_inhabited|inhabited pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.is_one|pos_num → bool
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.inc|pos_num → pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.ibelow|pos_num → Prop
|
2014-12-03 18:39:22 +00:00
|
|
|
pos_num.binduction_on|Π (n : pos_num), (Π (n : pos_num), pos_num.ibelow n → ?C n) → ?C n
|
2014-10-25 20:36:38 +00:00
|
|
|
pos_num.induction_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.succ|pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.bit1|pos_num → pos_num
|
|
|
|
|
pos_num.rec|?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → (Π (n : pos_num), ?C n)
|
|
|
|
|
pos_num.one|pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.below|pos_num → Type
|
2014-10-26 00:22:02 +00:00
|
|
|
pos_num.cases_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C (pos_num.bit0 a)) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.pred|pos_num → pos_num
|
|
|
|
|
pos_num.mul|pos_num → pos_num → pos_num
|
|
|
|
|
pos_num.no_confusion_type|Type → pos_num → pos_num → Type
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.num_bits|pos_num → pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.no_confusion|eq ?v1 ?v2 → pos_num.no_confusion_type ?P ?v1 ?v2
|
2014-10-25 18:32:26 +00:00
|
|
|
pos_num.rec_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
2014-12-03 18:39:22 +00:00
|
|
|
pos_num.brec_on|Π (n : pos_num), (Π (n : pos_num), pos_num.below n → ?C n) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.add|pos_num → pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num|Type
|
|
|
|
|
-- ENDFINDP
|
|
|
|
|
-- BEGINWAIT
|
|
|
|
|
-- ENDWAIT
|
|
|
|
|
-- BEGINWAIT
|
|
|
|
|
-- ENDWAIT
|
|
|
|
|
-- BEGINFINDP
|
|
|
|
|
pos_num.size|pos_num → pos_num
|
|
|
|
|
pos_num.bit0|pos_num → pos_num
|
|
|
|
|
pos_num.is_inhabited|inhabited pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.is_one|pos_num → bool
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.inc|pos_num → pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.ibelow|pos_num → Prop
|
2014-12-03 18:39:22 +00:00
|
|
|
pos_num.binduction_on|Π (n : pos_num), (Π (n : pos_num), pos_num.ibelow n → ?C n) → ?C n
|
2014-10-25 20:36:38 +00:00
|
|
|
pos_num.induction_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.succ|pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.bit1|pos_num → pos_num
|
|
|
|
|
pos_num.rec|?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → (Π (n : pos_num), ?C n)
|
|
|
|
|
pos_num.one|pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.below|pos_num → Type
|
2014-10-26 00:22:02 +00:00
|
|
|
pos_num.cases_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C (pos_num.bit0 a)) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.pred|pos_num → pos_num
|
|
|
|
|
pos_num.mul|pos_num → pos_num → pos_num
|
|
|
|
|
pos_num.no_confusion_type|Type → pos_num → pos_num → Type
|
|
|
|
|
pos_num.no_confusion|eq ?v1 ?v2 → pos_num.no_confusion_type ?P ?v1 ?v2
|
2014-10-25 18:32:26 +00:00
|
|
|
pos_num.rec_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
2014-12-03 18:39:22 +00:00
|
|
|
pos_num.brec_on|Π (n : pos_num), (Π (n : pos_num), pos_num.below n → ?C n) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.add|pos_num → pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num|Type
|
|
|
|
|
-- ENDFINDP
|
|
|
|
|
-- BEGINFINDP
|
|
|
|
|
pos_num.size|pos_num → pos_num
|
|
|
|
|
pos_num.bit0|pos_num → pos_num
|
|
|
|
|
pos_num.is_inhabited|inhabited pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.is_one|pos_num → bool
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.inc|pos_num → pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.ibelow|pos_num → Prop
|
2014-12-03 18:39:22 +00:00
|
|
|
pos_num.binduction_on|Π (n : pos_num), (Π (n : pos_num), pos_num.ibelow n → ?C n) → ?C n
|
2014-10-25 20:36:38 +00:00
|
|
|
pos_num.induction_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.succ|pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num.bit1|pos_num → pos_num
|
|
|
|
|
pos_num.rec|?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → (Π (n : pos_num), ?C n)
|
|
|
|
|
pos_num.one|pos_num
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.below|pos_num → Type
|
2014-10-26 00:22:02 +00:00
|
|
|
pos_num.cases_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C (pos_num.bit0 a)) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.pred|pos_num → pos_num
|
|
|
|
|
pos_num.mul|pos_num → pos_num → pos_num
|
|
|
|
|
pos_num.no_confusion_type|Type → pos_num → pos_num → Type
|
|
|
|
|
pos_num.no_confusion|eq ?v1 ?v2 → pos_num.no_confusion_type ?P ?v1 ?v2
|
2014-10-25 18:32:26 +00:00
|
|
|
pos_num.rec_on|Π (n : pos_num), ?C pos_num.one → (Π (a : pos_num), ?C a → ?C (pos_num.bit1 a)) → (Π (a : pos_num), ?C a → ?C (pos_num.bit0 a)) → ?C n
|
2014-12-03 18:39:22 +00:00
|
|
|
pos_num.brec_on|Π (n : pos_num), (Π (n : pos_num), pos_num.below n → ?C n) → ?C n
|
2014-12-01 05:16:01 +00:00
|
|
|
pos_num.add|pos_num → pos_num → pos_num
|
2014-09-15 17:25:07 +00:00
|
|
|
pos_num|Type
|
|
|
|
|
-- ENDFINDP
|
