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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, 3,  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
2instantiation4, 5, 6,  ⊢  
  :
3reference60  ⊢  
4theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
5instantiation48, 7, 8,  ⊢  
  : , :
6instantiation9, 10,  ⊢  
  : , :
7instantiation58, 11, 26,  ⊢  
  : , : , :
8instantiation58, 12, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.ordering.relax_less
10instantiation14, 15,  ⊢  
  : , :
11instantiation44, 25, 49  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
13instantiation16, 17  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
15instantiation28, 18, 19,  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
17theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
18instantiation20, 43, 21, 22, 23, 24*  ⊢  
  : , : , :
19instantiation35, 25, 49, 26,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
22instantiation58, 46, 27  ⊢  
  : , : , :
23instantiation28, 29, 30  ⊢  
  : , : , :
24instantiation31, 32, 33  ⊢  
  : , : , :
25instantiation48, 34, 52  ⊢  
  : , :
26assumption  ⊢  
27instantiation58, 51, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
29theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
30instantiation35, 52, 45, 41  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
32instantiation36, 38  ⊢  
  :
33instantiation37, 38, 39  ⊢  
  : , :
34instantiation58, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
36theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
37theorem  ⊢  
 proveit.numbers.addition.commutation
38instantiation58, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
40instantiation44, 52, 45  ⊢  
  : , :
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation58, 46, 47  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
45instantiation48, 49, 50  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
47instantiation58, 51, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
49instantiation58, 53, 54  ⊢  
  : , : , :
50instantiation55, 56  ⊢  
  :
51theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
52instantiation58, 59, 57  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
54theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
55theorem  ⊢  
 proveit.numbers.negation.int_closure
56instantiation58, 59, 60  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements