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^, 5^	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
2	reference	6	⊢
3	reference	70	⊢
4	instantiation	46, 6	⊢
	:
5	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
6	instantiation	17, 7, 8, 9	⊢
	: , :
7	instantiation	73, 54, 10	⊢
	: , : , :
8	instantiation	11, 47, 12	⊢
	: , :
9	instantiation	13, 14, 15	⊢
	: , : , :
10	instantiation	73, 62, 16	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
12	instantiation	17, 37, 47, 25	⊢
	: , :
13	theorem		⊢
	proveit.logic.equality.sub_left_side_into
14	instantiation	18, 53, 19	⊢
	: , :
15	instantiation	34, 20	⊢
	: , : , :
16	instantiation	73, 68, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
19	instantiation	73, 22, 23	⊢
	: , : , :
20	instantiation	24, 37, 47, 25, 26^*	⊢
	: , :
21	instantiation	73, 74, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
23	instantiation	28, 59, 29	⊢
	: , :
24	theorem		⊢
	proveit.numbers.division.div_as_mult
25	instantiation	30, 72	⊢
	:
26	instantiation	31, 32, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
28	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
29	instantiation	73, 71, 50	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	34, 35	⊢
	: , : , :
33	instantiation	36, 37, 38	⊢
	: , :
34	axiom		⊢
	proveit.logic.equality.substitution
35	instantiation	39, 40, 70, 41^*	⊢
	: , :
36	theorem		⊢
	proveit.numbers.multiplication.commutation
37	instantiation	73, 54, 42	⊢
	: , : , :
38	instantiation	73, 54, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
40	instantiation	73, 44, 45	⊢
	: , : , :
41	instantiation	46, 47	⊢
	:
42	instantiation	48, 49, 50	⊢
	: , : , :
43	instantiation	73, 62, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
45	instantiation	73, 52, 53	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
47	instantiation	73, 54, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	56, 57	⊢
	: , :
50	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
51	instantiation	73, 58, 59	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
53	instantiation	73, 60, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	73, 62, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
59	instantiation	64, 65, 66	⊢
	: , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
61	instantiation	73, 67, 72	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
63	instantiation	73, 68, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
65	instantiation	73, 71, 70	⊢
	: , : , :
66	instantiation	73, 71, 72	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	73, 74, 75	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
72	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements