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	reference	26	⊢
2	instantiation	3, 4, 5, 6, 7, 8	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
4	instantiation	74, 70, 9	⊢
	: , : , :
5	instantiation	10, 13	⊢
	: , :
6	instantiation	74, 70, 11	⊢
	: , : , :
7	instantiation	12, 13, 14, 15, 16	⊢
	: , : , :
8	instantiation	43, 18	⊢
	:
9	instantiation	17, 19, 20	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
11	instantiation	74, 29, 18	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
13	instantiation	74, 70, 19	⊢
	: , : , :
14	instantiation	74, 70, 20	⊢
	: , : , :
15	instantiation	21, 22, 23, 24, 25	⊢
	: , : , :
16	instantiation	26, 27	⊢
	: , :
17	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
18	instantiation	56, 57, 28	⊢
	: , :
19	instantiation	74, 29, 44	⊢
	: , : , :
20	instantiation	30, 49, 31, 32	⊢
	: , :
21	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
22	instantiation	74, 33, 34	⊢
	: , : , :
23	instantiation	74, 35, 58	⊢
	: , : , :
24	instantiation	74, 35, 36	⊢
	: , : , :
25	instantiation	37, 65, 38, 39, 40, 41, 42^*	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.ordering.relax_less
27	instantiation	43, 44	⊢
	:
28	instantiation	74, 67, 45	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
30	theorem		⊢
	proveit.numbers.division.div_rational_closure
31	instantiation	74, 72, 46	⊢
	: , : , :
32	instantiation	47, 60	⊢
	:
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
34	instantiation	74, 48, 69	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
36	instantiation	74, 67, 60	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
38	instantiation	74, 70, 49	⊢
	: , : , :
39	instantiation	50, 51, 53	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
41	instantiation	52, 53	⊢
	:
42	instantiation	54, 55	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
44	instantiation	56, 57, 58	⊢
	: , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
46	instantiation	74, 59, 60	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
49	instantiation	74, 72, 61	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
51	instantiation	62, 63	⊢
	: , :
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
53	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
54	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
55	instantiation	74, 64, 65	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
57	instantiation	74, 67, 66	⊢
	: , : , :
58	instantiation	74, 67, 68	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
60	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
61	instantiation	74, 75, 69	⊢
	: , : , :
62	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
65	instantiation	74, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
71	instantiation	74, 72, 73	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
73	instantiation	74, 75, 76	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements