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, 4, 16, 5, 6, 7^, 8^	, ⊢
	: , : , : , :
3	theorem		⊢
	proveit.numbers.division.prod_of_fracs
4	instantiation	9, 10, 11	⊢
	: , : , :
5	instantiation	73, 13, 12	⊢
	: , : , :
6	instantiation	73, 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	73, 24, 23	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
14	instantiation	73, 24, 25	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.division.frac_one_denom
16	instantiation	73, 50, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
18	instantiation	73, 50, 27	⊢
	: , : , :
19	instantiation	41, 34, 35	⊢
	: , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	29, 75, 68, 30, 33, 31, 28, 34, 35	⊢
	: , : , : , : , : , :
22	instantiation	29, 30, 68, 31, 32, 33, 42, 43, 34, 35	⊢
	: , : , : , : , : , :
23	instantiation	73, 37, 36	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
25	instantiation	73, 37, 38	⊢
	: , : , :
26	instantiation	73, 55, 39	⊢
	: , : , :
27	instantiation	73, 55, 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	73, 50, 45	⊢
	: , : , :
36	instantiation	73, 46, 70	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	73, 46, 47	⊢
	: , : , :
39	instantiation	73, 63, 48	⊢
	: , : , :
40	instantiation	73, 63, 66	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
42	instantiation	73, 50, 49	⊢
	: , : , :
43	instantiation	73, 50, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45	instantiation	73, 55, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
48	instantiation	73, 53, 54	⊢
	: , : , :
49	instantiation	73, 55, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
51	instantiation	73, 57, 58	⊢
	: , : , :
52	instantiation	73, 63, 59	⊢
	: , : , :
53	instantiation	60, 61, 62	⊢
	: , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	73, 63, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
59	assumption		⊢
60	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
61	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
62	instantiation	65, 66, 67	⊢
	: , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	73, 74, 68	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
66	instantiation	73, 69, 70	⊢
	: , : , :
67	instantiation	71, 72	⊢
	:
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
70	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
71	theorem		⊢
	proveit.numbers.negation.int_closure
72	instantiation	73, 74, 75	⊢
	: , : , :
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.nat1
^*equality replacement requirements