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^*	, ⊢
	: , :
1	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
2	reference	58	⊢
3	instantiation	79, 61, 5	, ⊢
	: , : , :
4	instantiation	9, 6, 7	⊢
	: , : , :
5	instantiation	79, 53, 8	, ⊢
	: , : , :
6	instantiation	9, 10, 11	⊢
	: , : , :
7	instantiation	12, 13, 14, 15	⊢
	: , : , : , :
8	instantiation	79, 16, 17	, ⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.sub_right_side_into
10	instantiation	18, 32, 33, 19, 20	⊢
	: , : , : , : , :
11	instantiation	39, 21, 22	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	48, 23	⊢
	: , : , :
14	instantiation	48, 24	⊢
	: , : , :
15	instantiation	57, 33	⊢
	:
16	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
17	instantiation	25, 26, 36	, ⊢
	: , :
18	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
19	instantiation	79, 28, 27	⊢
	: , : , :
20	instantiation	79, 28, 29	⊢
	: , : , :
21	instantiation	48, 30	⊢
	: , : , :
22	instantiation	48, 31	⊢
	: , : , :
23	instantiation	50, 32	⊢
	:
24	instantiation	50, 33	⊢
	:
25	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
26	instantiation	34, 54, 35	, ⊢
	:
27	instantiation	79, 37, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
29	instantiation	79, 37, 38	⊢
	: , : , :
30	instantiation	39, 40, 41	⊢
	: , : , :
31	instantiation	48, 42	⊢
	: , : , :
32	instantiation	79, 61, 43	⊢
	: , : , :
33	instantiation	79, 61, 44	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
35	assumption		⊢
36	instantiation	79, 46, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
38	instantiation	79, 46, 47	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	48, 49	⊢
	: , : , :
41	instantiation	50, 58	⊢
	:
42	instantiation	51, 58	⊢
	:
43	instantiation	79, 53, 52	⊢
	: , : , :
44	instantiation	79, 53, 54	⊢
	: , : , :
45	instantiation	79, 55, 67	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
47	instantiation	79, 55, 56	⊢
	: , : , :
48	axiom		⊢
	proveit.logic.equality.substitution
49	instantiation	57, 58	⊢
	:
50	theorem		⊢
	proveit.numbers.division.frac_one_denom
51	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
52	instantiation	79, 59, 74	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	79, 59, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
58	instantiation	79, 61, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	79, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
62	instantiation	65, 66, 67	⊢
	: , : , :
63	instantiation	68, 69, 76	⊢
	: , :
64	assumption		⊢
65	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
66	instantiation	70, 71	⊢
	: , :
67	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
68	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
69	instantiation	72, 73, 74	⊢
	: , :
70	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
72	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
73	instantiation	75, 76	⊢
	:
74	instantiation	79, 77, 78	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.negation.int_closure
76	instantiation	79, 80, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
79	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
81	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements