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.division.frac_cancel_left
2	instantiation	76, 7, 6	⊢
	: , : , :
3	instantiation	76, 7, 8	⊢
	: , : , :
4	instantiation	76, 19, 9	⊢
	: , : , :
5	instantiation	10, 11	⊢
	:
6	instantiation	76, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
8	instantiation	76, 14, 15	⊢
	: , : , :
9	instantiation	16, 17, 49, 18	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
11	instantiation	76, 19, 35	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
13	instantiation	20, 21, 22	⊢
	: , :
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
15	instantiation	76, 53, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
17	instantiation	24, 25, 26	⊢
	: , :
18	instantiation	27, 32	⊢
	:
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
20	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
21	instantiation	76, 28, 29	⊢
	: , : , :
22	instantiation	30, 31, 75	⊢
	: , : , :
23	instantiation	76, 60, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	instantiation	33, 34, 35, 36	⊢
	: , :
26	instantiation	37, 38	⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
29	instantiation	76, 39, 59	⊢
	: , : , :
30	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
31	instantiation	40, 41	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
33	theorem		⊢
	proveit.numbers.division.div_real_closure
34	instantiation	76, 55, 42	⊢
	: , : , :
35	instantiation	76, 55, 43	⊢
	: , : , :
36	instantiation	44, 45, 46	⊢
	: , :
37	theorem		⊢
	proveit.numbers.negation.real_closure
38	instantiation	47, 48, 49, 50	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
40	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42	instantiation	76, 61, 51	⊢
	: , : , :
43	instantiation	76, 61, 66	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
45	instantiation	76, 53, 52	⊢
	: , : , :
46	instantiation	76, 53, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
49	instantiation	76, 55, 56	⊢
	: , : , :
50	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
51	instantiation	76, 57, 58	⊢
	: , : , :
52	instantiation	76, 60, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
54	instantiation	76, 60, 75	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	76, 61, 72	⊢
	: , : , :
57	instantiation	62, 63, 64	⊢
	: , :
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
63	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
64	instantiation	65, 66, 67	⊢
	: , :
65	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
66	instantiation	68, 69, 70	⊢
	: , :
67	instantiation	71, 72	⊢
	:
68	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
69	instantiation	76, 77, 73	⊢
	: , : , :
70	instantiation	76, 74, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.negation.int_closure
72	instantiation	76, 77, 78	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
75	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements