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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, 4, 5, 6*, 7*  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
2instantiation57, 47, 8  ⊢  
  : , : , :
3theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
4reference45  ⊢  
5instantiation9, 10  ⊢  
  :
6instantiation13, 11, 12  ⊢  
  : , : , :
7instantiation13, 14, 15  ⊢  
  : , : , :
8instantiation57, 50, 16  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
10instantiation17, 56, 54  ⊢  
  : , :
11instantiation20, 49, 56, 34, 21, 35, 18, 42, 24  ⊢  
  : , : , : , : , : , :
12instantiation19, 34, 56, 35, 21, 42, 24  ⊢  
  : , : , : , :
13axiom  ⊢  
 proveit.logic.equality.equals_transitivity
14instantiation20, 49, 56, 34, 21, 35, 42, 24  ⊢  
  : , : , : , : , : , :
15instantiation22, 34, 56, 49, 35, 23, 42, 24, 25*  ⊢  
  : , : , : , : , : , :
16instantiation26, 51, 27  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
19theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
20theorem  ⊢  
 proveit.numbers.addition.disassociation
21instantiation39  ⊢  
  : , :
22theorem  ⊢  
 proveit.numbers.addition.association
23instantiation39  ⊢  
  : , :
24instantiation28, 37  ⊢  
  :
25instantiation29, 30, 31*  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
27instantiation32, 46  ⊢  
  :
28theorem  ⊢  
 proveit.numbers.negation.complex_closure
29theorem  ⊢  
 proveit.logic.equality.equals_reversal
30instantiation33, 34, 56, 49, 35, 36, 37, 42, 38*  ⊢  
  : , : , : , : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
32theorem  ⊢  
 proveit.numbers.negation.int_closure
33theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
34axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
35theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36instantiation39  ⊢  
  : , :
37instantiation57, 44, 40  ⊢  
  : , : , :
38instantiation41, 42  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40instantiation57, 47, 43  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
42instantiation57, 44, 45  ⊢  
  : , : , :
43instantiation57, 50, 46  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
45instantiation57, 47, 48  ⊢  
  : , : , :
46instantiation57, 55, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation57, 50, 51  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation52, 53, 54  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
53instantiation57, 55, 56  ⊢  
  : , : , :
54instantiation57, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
59assumption  ⊢  
*equality replacement requirements