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	⊢
	:
1	reference	42	⊢
2	instantiation	13, 3, 4, 5	⊢
	: , :
3	instantiation	69, 50, 6	⊢
	: , : , :
4	instantiation	7, 43, 8	⊢
	: , :
5	instantiation	9, 10, 11	⊢
	: , : , :
6	instantiation	69, 58, 12	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
8	instantiation	13, 33, 43, 21	⊢
	: , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	14, 49, 15	⊢
	: , :
11	instantiation	30, 16	⊢
	: , : , :
12	instantiation	69, 64, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.division.div_complex_closure
14	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
15	instantiation	69, 18, 19	⊢
	: , : , :
16	instantiation	20, 33, 43, 21, 22^*	⊢
	: , :
17	instantiation	69, 70, 23	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
19	instantiation	24, 55, 25	⊢
	: , :
20	theorem		⊢
	proveit.numbers.division.div_as_mult
21	instantiation	26, 68	⊢
	:
22	instantiation	27, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
24	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
25	instantiation	69, 67, 46	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	30, 31	⊢
	: , : , :
29	instantiation	32, 33, 34	⊢
	: , :
30	axiom		⊢
	proveit.logic.equality.substitution
31	instantiation	35, 36, 66, 37^*	⊢
	: , :
32	theorem		⊢
	proveit.numbers.multiplication.commutation
33	instantiation	69, 50, 38	⊢
	: , : , :
34	instantiation	69, 50, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
36	instantiation	69, 40, 41	⊢
	: , : , :
37	instantiation	42, 43	⊢
	:
38	instantiation	44, 45, 46	⊢
	: , : , :
39	instantiation	69, 58, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
41	instantiation	69, 48, 49	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
43	instantiation	69, 50, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
45	instantiation	52, 53	⊢
	: , :
46	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
47	instantiation	69, 54, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49	instantiation	69, 56, 57	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	69, 58, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
55	instantiation	60, 61, 62	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	69, 63, 68	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	69, 64, 65	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
61	instantiation	69, 67, 66	⊢
	: , : , :
62	instantiation	69, 67, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	69, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements