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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2instantiation3, 4, 37, 41, 5, 6, 7*  ⊢  
  : , : , : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
4instantiation52, 8, 9  ⊢  
  : , : , :
5instantiation10, 37, 11  ⊢  
  : , :
6instantiation12, 13  ⊢  
  : , :
7instantiation14, 15  ⊢  
  :
8theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
9instantiation52, 16, 17  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
11instantiation52, 46, 18  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.logic.equality.equals_reversal
13instantiation19, 20, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
15instantiation52, 40, 22  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
17theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
18instantiation52, 50, 23  ⊢  
  : , : , :
19axiom  ⊢  
 proveit.logic.equality.equals_transitivity
20instantiation24, 54, 45, 25, 26, 27, 36, 30, 28  ⊢  
  : , : , : , : , : , :
21instantiation29, 36, 30, 31  ⊢  
  : , : , :
22instantiation52, 46, 32  ⊢  
  : , : , :
23instantiation33, 51  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.addition.disassociation
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26instantiation34  ⊢  
  : , :
27theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28instantiation35, 36  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
30instantiation52, 40, 37  ⊢  
  : , : , :
31instantiation38  ⊢  
  :
32instantiation52, 50, 39  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.negation.int_closure
34theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35theorem  ⊢  
 proveit.numbers.negation.complex_closure
36instantiation52, 40, 41  ⊢  
  : , : , :
37instantiation42, 43, 44  ⊢  
  : , : , :
38axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
39instantiation52, 53, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41instantiation52, 46, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
43instantiation48, 49  ⊢  
  : , :
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
47instantiation52, 50, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation52, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements