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.addition.strong_bound_via_left_term_bound
2	instantiation	81, 76, 8	⊢
	: , : , :
3	instantiation	9, 37, 12	⊢
	: , :
4	instantiation	81, 76, 10	⊢
	: , : , :
5	instantiation	11, 37, 12, 69, 13, 14	⊢
	: , : , :
6	instantiation	46, 15, 16	⊢
	: , : , :
7	instantiation	46, 17, 18	⊢
	: , : , :
8	instantiation	81, 79, 27	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
10	instantiation	19, 45, 72	⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
12	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
13	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
14	instantiation	20, 51	⊢
	:
15	instantiation	24, 21	⊢
	: , : , :
16	instantiation	22, 23	⊢
	:
17	instantiation	24, 25	⊢
	: , : , :
18	instantiation	26, 75, 80, 27, 28^, 29^	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
20	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
21	instantiation	30, 32	⊢
	:
22	theorem		⊢
	proveit.numbers.addition.elim_zero_left
23	instantiation	31, 64	⊢
	:
24	axiom		⊢
	proveit.logic.equality.substitution
25	instantiation	70, 32	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
27	instantiation	33, 75	⊢
	:
28	instantiation	43, 64, 39, 34^*	⊢
	: , :
29	instantiation	46, 35, 36	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
31	theorem		⊢
	proveit.numbers.negation.complex_closure
32	instantiation	81, 73, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.negation.int_closure
34	instantiation	38, 64, 39	⊢
	:
35	instantiation	52, 83, 40, 41, 42, 65	⊢
	: , : , : , :
36	instantiation	43, 64, 71, 44	⊢
	: , :
37	instantiation	81, 76, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
39	instantiation	49, 66	⊢
	:
40	instantiation	62	⊢
	: , :
41	instantiation	62	⊢
	: , :
42	instantiation	46, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
44	instantiation	49, 68	⊢
	:
45	instantiation	81, 50, 51	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_transitivity
47	instantiation	52, 83, 53, 54, 55, 56	⊢
	: , : , : , :
48	instantiation	57, 64, 71, 58	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
51	instantiation	59, 60, 61	⊢
	: , :
52	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
53	instantiation	62	⊢
	: , :
54	instantiation	62	⊢
	: , :
55	instantiation	70, 64	⊢
	:
56	instantiation	63, 71, 64, 65^*	⊢
	: , :
57	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
58	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
59	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
60	instantiation	81, 67, 66	⊢
	: , : , :
61	instantiation	81, 67, 68	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
64	instantiation	81, 73, 69	⊢
	: , : , :
65	instantiation	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	instantiation	81, 76, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
71	instantiation	81, 73, 74	⊢
	: , : , :
72	instantiation	81, 79, 75	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	instantiation	81, 76, 77	⊢
	: , : , :
75	instantiation	81, 82, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
77	instantiation	81, 79, 80	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	instantiation	81, 82, 83	⊢
	: , : , :
81	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements