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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
0modus ponens1, 2  ⊢  
1instantiation3  ⊢  
  : , : , :
2generalization4  ⊢  
3theorem  ⊢  
 proveit.numbers.summation.summation_real_closure
4instantiation5, 58, 6, 7,  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.division.div_real_closure
6instantiation8, 9, 75,  ⊢  
  : , :
7instantiation10, 11,  ⊢  
  :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
9instantiation12, 13, 14,  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11instantiation15, 16, 75,  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
13instantiation73, 61, 17,  ⊢  
  : , : , :
14instantiation18, 58  ⊢  
  :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
16instantiation19, 20, 21,  ⊢  
  :
17instantiation73, 66, 22,  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.negation.real_closure
19theorem  ⊢  
 proveit.numbers.number_sets.integers.nonneg_int_is_natural
20instantiation63, 22, 23,  ⊢  
  : , :
21instantiation24, 25,  ⊢  
  : , :
22instantiation73, 26, 41,  ⊢  
  : , : , :
23instantiation73, 27, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.ordering.relax_less
25instantiation29, 30,  ⊢  
  : , :
26instantiation59, 40, 64  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
28instantiation31, 32  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
30instantiation43, 33, 34,  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
32theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
33instantiation35, 58, 36, 37, 38, 39*  ⊢  
  : , : , :
34instantiation50, 40, 64, 41,  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
37instantiation73, 61, 42  ⊢  
  : , : , :
38instantiation43, 44, 45  ⊢  
  : , : , :
39instantiation46, 47, 48  ⊢  
  : , : , :
40instantiation63, 49, 67  ⊢  
  : , :
41assumption  ⊢  
42instantiation73, 66, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
44theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
45instantiation50, 67, 60, 56  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
47instantiation51, 53  ⊢  
  :
48instantiation52, 53, 54  ⊢  
  : , :
49instantiation73, 55, 56  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
51theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
52theorem  ⊢  
 proveit.numbers.addition.commutation
53instantiation73, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
55instantiation59, 67, 60  ⊢  
  : , :
56assumption  ⊢  
57theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
58instantiation73, 61, 62  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
60instantiation63, 64, 65  ⊢  
  : , :
61theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
62instantiation73, 66, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
64instantiation73, 68, 69  ⊢  
  : , : , :
65instantiation70, 71  ⊢  
  :
66theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
67instantiation73, 74, 72  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
69theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
70theorem  ⊢  
 proveit.numbers.negation.int_closure
71instantiation73, 74, 75  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
73theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
75theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements