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	reference	25	⊢
2	instantiation	4, 5	, ⊢
	: , : , :
3	instantiation	6, 10, 7, 8	, , ⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	9, 10, 12, 13	, ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.exponentiation.complex_power_of_complex_power
7	instantiation	11, 12, 13	, ⊢
	: , :
8	instantiation	58, 48, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
11	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
12	instantiation	17, 15, 16	⊢
	: , : , :
13	instantiation	17, 18, 19	⊢
	: , : , :
14	instantiation	58, 52, 20	⊢
	: , : , :
15	instantiation	41, 32, 21	⊢
	: , :
16	instantiation	25, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	41, 32, 24	⊢
	: , :
19	instantiation	25, 26, 27	⊢
	: , : , :
20	instantiation	58, 56, 28	⊢
	: , : , :
21	instantiation	41, 38, 30	⊢
	: , :
22	instantiation	33, 31, 60, 34, 29, 35, 32, 38, 30	⊢
	: , : , : , : , : , :
23	instantiation	33, 34, 60, 35, 36, 29, 42, 43, 38, 30	⊢
	: , : , : , : , : , :
24	instantiation	41, 38, 39	⊢
	: , :
25	axiom		⊢
	proveit.logic.equality.equals_transitivity
26	instantiation	33, 31, 60, 34, 37, 35, 32, 38, 39	⊢
	: , : , : , : , : , :
27	instantiation	33, 34, 60, 35, 36, 37, 42, 43, 38, 39	⊢
	: , : , : , : , : , :
28	assumption		⊢
29	instantiation	44	⊢
	: , :
30	instantiation	58, 48, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
32	instantiation	41, 42, 43	⊢
	: , :
33	theorem		⊢
	proveit.numbers.multiplication.disassociation
34	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
35	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
36	instantiation	44	⊢
	: , :
37	instantiation	44	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
39	instantiation	58, 48, 45	⊢
	: , : , :
40	instantiation	58, 52, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
42	instantiation	58, 48, 47	⊢
	: , : , :
43	instantiation	58, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	instantiation	58, 54, 50	⊢
	: , : , :
46	instantiation	58, 56, 51	⊢
	: , : , :
47	instantiation	58, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	58, 54, 55	⊢
	: , : , :
50	assumption		⊢
51	assumption		⊢
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	58, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
57	instantiation	58, 59, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat2