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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	3, 16, 4, 5, 6, 7^, 8^	, ⊢
	: , : , : , :
3	theorem		⊢
	proveit.numbers.division.prod_of_fracs
4	instantiation	9, 10, 11	⊢
	: , : , :
5	instantiation	76, 13, 12	⊢
	: , : , :
6	instantiation	76, 13, 14	⊢
	: , : , :
7	instantiation	15, 16	⊢
	:
8	instantiation	17, 18	⊢
	:
9	theorem		⊢
	proveit.logic.equality.sub_right_side_into
10	instantiation	41, 28, 19	⊢
	: , :
11	instantiation	20, 21, 22	⊢
	: , : , :
12	instantiation	76, 24, 23	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
14	instantiation	76, 24, 25	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.division.frac_one_denom
16	instantiation	76, 50, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
18	instantiation	76, 50, 27	⊢
	: , : , :
19	instantiation	41, 34, 35	⊢
	: , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	29, 78, 63, 30, 33, 31, 28, 34, 35	⊢
	: , : , : , : , : , :
22	instantiation	29, 30, 63, 31, 32, 33, 42, 43, 34, 35	⊢
	: , : , : , : , : , :
23	instantiation	76, 37, 36	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
25	instantiation	76, 37, 38	⊢
	: , : , :
26	instantiation	76, 54, 39	⊢
	: , : , :
27	instantiation	76, 54, 40	⊢
	: , : , :
28	instantiation	41, 42, 43	⊢
	: , :
29	theorem		⊢
	proveit.numbers.multiplication.disassociation
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	instantiation	44	⊢
	: , :
33	instantiation	44	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
35	instantiation	76, 50, 45	⊢
	: , : , :
36	instantiation	76, 47, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	76, 47, 73	⊢
	: , : , :
39	instantiation	76, 59, 48	⊢
	: , : , :
40	instantiation	76, 59, 70	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
42	instantiation	76, 50, 49	⊢
	: , : , :
43	instantiation	76, 50, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	instantiation	76, 54, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
48	instantiation	76, 61, 53	⊢
	: , : , :
49	instantiation	76, 54, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	76, 56, 57	⊢
	: , : , :
52	instantiation	76, 59, 58	⊢
	: , : , :
53	assumption		⊢
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	76, 59, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
58	instantiation	76, 61, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	76, 77, 63	⊢
	: , : , :
61	instantiation	64, 65, 66	⊢
	: , :
62	instantiation	67, 68, 73	⊢
	: , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
64	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
65	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
66	instantiation	69, 70, 71	⊢
	: , :
67	theorem		⊢
	proveit.numbers.modular.mod_natpos_in_interval
68	assumption		⊢
69	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
70	instantiation	76, 72, 73	⊢
	: , : , :
71	instantiation	74, 75	⊢
	:
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
73	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
74	theorem		⊢
	proveit.numbers.negation.int_closure
75	instantiation	76, 77, 78	⊢
	: , : , :
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