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Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
2instantiation13, 3, 4,  ⊢  
  : , : , :
3instantiation5, 28, 6, 7, 8, 9*  ⊢  
  : , : , :
4instantiation20, 10, 34, 11,  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
6theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
7instantiation43, 31, 12  ⊢  
  : , : , :
8instantiation13, 14, 15  ⊢  
  : , : , :
9instantiation16, 17, 18  ⊢  
  : , : , :
10instantiation33, 19, 37  ⊢  
  : , :
11assumption  ⊢  
12instantiation43, 36, 19  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
14theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
15instantiation20, 37, 30, 26  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
17instantiation21, 23  ⊢  
  :
18instantiation22, 23, 24  ⊢  
  : , :
19instantiation43, 25, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
21theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
22theorem  ⊢  
 proveit.numbers.addition.commutation
23instantiation43, 27, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
25instantiation29, 37, 30  ⊢  
  : , :
26assumption  ⊢  
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
28instantiation43, 31, 32  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
30instantiation33, 34, 35  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
32instantiation43, 36, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
34instantiation43, 38, 39  ⊢  
  : , : , :
35instantiation40, 41  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
37instantiation43, 44, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
39theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
40theorem  ⊢  
 proveit.numbers.negation.int_closure
41instantiation43, 44, 45  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
43theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements