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 type	requirements	statement
0	instantiation	1, 2, 3	, , ⊢
	: , :
1	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
2	instantiation	55, 45, 4	⊢
	: , : , :
3	instantiation	38, 5, 6	, , ⊢
	: , :
4	instantiation	55, 51, 7	⊢
	: , : , :
5	instantiation	8, 9, 10	, ⊢
	: , :
6	instantiation	55, 45, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
8	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
9	instantiation	14, 12, 13	⊢
	: , : , :
10	instantiation	14, 15, 16	⊢
	: , : , :
11	instantiation	55, 49, 17	⊢
	: , : , :
12	instantiation	38, 29, 18	⊢
	: , :
13	instantiation	22, 19, 20	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	38, 29, 21	⊢
	: , :
16	instantiation	22, 23, 24	⊢
	: , : , :
17	instantiation	55, 53, 25	⊢
	: , : , :
18	instantiation	38, 35, 27	⊢
	: , :
19	instantiation	30, 28, 57, 31, 26, 32, 29, 35, 27	⊢
	: , : , : , : , : , :
20	instantiation	30, 31, 57, 32, 33, 26, 39, 40, 35, 27	⊢
	: , : , : , : , : , :
21	instantiation	38, 35, 36	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	30, 28, 57, 31, 34, 32, 29, 35, 36	⊢
	: , : , : , : , : , :
24	instantiation	30, 31, 57, 32, 33, 34, 39, 40, 35, 36	⊢
	: , : , : , : , : , :
25	assumption		⊢
26	instantiation	41	⊢
	: , :
27	instantiation	55, 45, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	instantiation	38, 39, 40	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.disassociation
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	41	⊢
	: , :
34	instantiation	41	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
36	instantiation	55, 45, 42	⊢
	: , : , :
37	instantiation	55, 49, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
39	instantiation	55, 45, 44	⊢
	: , : , :
40	instantiation	55, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	instantiation	55, 51, 47	⊢
	: , : , :
43	instantiation	55, 53, 48	⊢
	: , : , :
44	instantiation	55, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	instantiation	55, 51, 52	⊢
	: , : , :
47	assumption		⊢
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	55, 53, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2