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