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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*, ,  ⊢  
  : , : , : , :
1reference10  ⊢  
2instantiation7, 6, ,  ⊢  
  : , : , :
3instantiation7, 8, ,  ⊢  
  : , : , :
4instantiation15, 9, ,  ⊢  
  : , :
5instantiation10, 11, 12, 13,  ⊢  
  : , : , : , :
6instantiation15, 14, ,  ⊢  
  : , :
7axiom  ⊢  
 proveit.logic.equality.substitution
8instantiation15, 16, ,  ⊢  
  : , :
9instantiation17, 74, 77, 24, 18, 25, 19, 33, 35, ,  ⊢  
  : , : , : , : , : , :
10theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
11instantiation20, 24, 77, 74, 25, 21, 39, 40, 35,  ⊢  
  : , : , : , : , : , :
12instantiation20, 77, 24, 21, 22, 25, 39, 40, 45, 41,  ⊢  
  : , : , : , : , : , :
13instantiation23, 74, 24, 25, 39, 45, 41,  ⊢  
  : , : , : , : , : , : , : , :
14instantiation27, 39, 33, 30, 31, 26*, ,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.logic.equality.equals_reversal
16instantiation27, 39, 35, 30, 31, 28*, ,  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
18instantiation32  ⊢  
  : , :
19instantiation29, 39, 30, 31,  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.addition.disassociation
21instantiation32  ⊢  
  : , :
22instantiation32  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_general_rev
24axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
25theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26instantiation34, 33,  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.division.mult_frac_left
28instantiation34, 35,  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.division.div_complex_closure
30instantiation54, 39, 36  ⊢  
  : , :
31instantiation37, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33instantiation54, 39, 40,  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
35instantiation54, 45, 41,  ⊢  
  : , :
36instantiation46, 51  ⊢  
  :
37theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
38instantiation42, 43  ⊢  
  : , :
39instantiation75, 59, 44  ⊢  
  : , : , :
40instantiation46, 45,  ⊢  
  :
41instantiation46, 47,  ⊢  
  :
42theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
43assumption  ⊢  
44instantiation75, 62, 48  ⊢  
  : , : , :
45instantiation50, 51, 49,  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.negation.complex_closure
47instantiation50, 51, 52,  ⊢  
  : , :
48instantiation75, 69, 68  ⊢  
  : , : , :
49instantiation75, 59, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
51assumption  ⊢  
52instantiation54, 55, 56  ⊢  
  : , :
53instantiation75, 62, 57  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
55instantiation75, 59, 58  ⊢  
  : , : , :
56instantiation75, 59, 60  ⊢  
  : , : , :
57instantiation75, 69, 61  ⊢  
  : , : , :
58instantiation75, 62, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
60instantiation64, 65, 73  ⊢  
  : , : , :
61instantiation66, 67, 68  ⊢  
  : , :
62theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
63instantiation75, 69, 70  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
65instantiation71, 72  ⊢  
  : , :
66theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
67instantiation75, 76, 73  ⊢  
  : , : , :
68instantiation75, 76, 74  ⊢  
  : , : , :
69theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
70instantiation75, 76, 77  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
72theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_within_real
73assumption  ⊢  
74theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
75theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
77theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements