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, 6^, 7^	, ⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.division.prod_of_fracs
2	reference	15	⊢
3	instantiation	8, 9, 10	⊢
	: , : , :
4	instantiation	75, 12, 11	⊢
	: , : , :
5	instantiation	75, 12, 13	⊢
	: , : , :
6	instantiation	14, 15	⊢
	:
7	instantiation	16, 17	⊢
	:
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	40, 27, 18	⊢
	: , :
10	instantiation	19, 20, 21	⊢
	: , : , :
11	instantiation	75, 23, 22	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
13	instantiation	75, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.division.frac_one_denom
15	instantiation	75, 49, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
17	instantiation	75, 49, 26	⊢
	: , : , :
18	instantiation	40, 33, 34	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	28, 77, 62, 29, 32, 30, 27, 33, 34	⊢
	: , : , : , : , : , :
21	instantiation	28, 29, 62, 30, 31, 32, 41, 42, 33, 34	⊢
	: , : , : , : , : , :
22	instantiation	75, 36, 35	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
24	instantiation	75, 36, 37	⊢
	: , : , :
25	instantiation	75, 53, 38	⊢
	: , : , :
26	instantiation	75, 53, 39	⊢
	: , : , :
27	instantiation	40, 41, 42	⊢
	: , :
28	theorem		⊢
	proveit.numbers.multiplication.disassociation
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	43	⊢
	: , :
32	instantiation	43	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
34	instantiation	75, 49, 44	⊢
	: , : , :
35	instantiation	75, 46, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37	instantiation	75, 46, 72	⊢
	: , : , :
38	instantiation	75, 58, 47	⊢
	: , : , :
39	instantiation	75, 58, 69	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
41	instantiation	75, 49, 48	⊢
	: , : , :
42	instantiation	75, 49, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44	instantiation	75, 53, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
47	instantiation	75, 60, 52	⊢
	: , : , :
48	instantiation	75, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	75, 55, 56	⊢
	: , : , :
51	instantiation	75, 58, 57	⊢
	: , : , :
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	75, 58, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
57	instantiation	75, 60, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	75, 76, 62	⊢
	: , : , :
60	instantiation	63, 64, 65	⊢
	: , :
61	instantiation	66, 67, 72	⊢
	: , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
63	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
64	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
65	instantiation	68, 69, 70	⊢
	: , :
66	theorem		⊢
	proveit.numbers.modular.mod_natpos_in_interval
67	assumption		⊢
68	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
69	instantiation	75, 71, 72	⊢
	: , : , :
70	instantiation	73, 74	⊢
	:
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
72	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
73	theorem		⊢
	proveit.numbers.negation.int_closure
74	instantiation	75, 76, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements