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	42	⊢
2	instantiation	13, 4	, ⊢
	: , : , :
3	instantiation	15, 5	, , , , ⊢
	: , :
4	instantiation	42, 6, 7	, ⊢
	: , : , :
5	instantiation	8, 9, 10, 32, 11, 12	, , , , ⊢
	: , : , :
6	instantiation	13, 14	, ⊢
	: , : , :
7	instantiation	15, 16	, ⊢
	: , :
8	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
9	instantiation	17, 25, 26	⊢
	: , :
10	instantiation	72, 63, 18	, ⊢
	: , : , :
11	instantiation	19, 25, 26, 27	⊢
	: , :
12	assumption		⊢
13	axiom		⊢
	proveit.logic.equality.substitution
14	instantiation	20, 51, 21, 48, 52, 22, 58, 59, 55, 56, 23	, ⊢
	: , : , : , : , : , :
15	theorem		⊢
	proveit.logic.equality.equals_reversal
16	instantiation	24, 25, 26, 27	, ⊢
	: , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
18	instantiation	28, 29, 30	, ⊢
	: , :
19	theorem		⊢
	proveit.numbers.exponentiation.exp_not_eq_zero
20	theorem		⊢
	proveit.numbers.multiplication.association
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
22	instantiation	31	⊢
	: , : , : , :
23	instantiation	72, 63, 32	⊢
	: , : , :
24	instantiation	33, 47	⊢
	:
25	instantiation	72, 63, 34	⊢
	: , : , :
26	instantiation	35, 36, 37	⊢
	: , : , :
27	instantiation	38, 39	⊢
	:
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	assumption		⊢
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
32	instantiation	72, 66, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_exp
34	instantiation	72, 68, 46	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.sub_right_side_into
36	instantiation	57, 49, 41	⊢
	: , :
37	instantiation	42, 43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
39	instantiation	72, 45, 46	⊢
	: , : , :
40	instantiation	72, 70, 47	⊢
	: , : , :
41	instantiation	57, 55, 56	⊢
	: , :
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	50, 48, 74, 51, 54, 52, 49, 55, 56	⊢
	: , : , : , : , : , :
44	instantiation	50, 51, 74, 52, 53, 54, 58, 59, 55, 56	⊢
	: , : , : , : , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
47	assumption		⊢
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
49	instantiation	57, 58, 59	⊢
	: , :
50	theorem		⊢
	proveit.numbers.multiplication.disassociation
51	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
52	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
53	instantiation	60	⊢
	: , :
54	instantiation	60	⊢
	: , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
56	instantiation	72, 63, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
58	instantiation	72, 63, 62	⊢
	: , : , :
59	instantiation	72, 63, 64	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
61	instantiation	72, 68, 65	⊢
	: , : , :
62	instantiation	72, 66, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	72, 68, 69	⊢
	: , : , :
65	assumption		⊢
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	72, 70, 71	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
71	instantiation	72, 73, 74	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2