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	reference	34	⊢
3	instantiation	8, 34, 11	⊢
	: , :
4	instantiation	75, 71, 9	⊢
	: , : , :
5	instantiation	10, 34, 11, 12, 13, 14	⊢
	: , : , :
6	instantiation	43, 15, 16	⊢
	: , : , :
7	instantiation	43, 17, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
9	instantiation	19, 42, 20	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	instantiation	75, 71, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
14	instantiation	21, 50	⊢
	:
15	instantiation	24, 22	⊢
	: , : , :
16	instantiation	23, 30	⊢
	:
17	instantiation	24, 25	⊢
	: , : , :
18	instantiation	26, 28, 74, 27^*	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
20	instantiation	75, 73, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
22	instantiation	29, 30	⊢
	:
23	theorem		⊢
	proveit.numbers.addition.elim_zero_left
24	axiom		⊢
	proveit.logic.equality.substitution
25	instantiation	62, 30	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
27	instantiation	43, 31, 32	⊢
	: , : , :
28	instantiation	75, 76, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
30	instantiation	75, 68, 34	⊢
	: , : , :
31	instantiation	51, 77, 35, 36, 37, 38	⊢
	: , : , : , :
32	instantiation	39, 40, 41	⊢
	:
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
34	instantiation	75, 71, 42	⊢
	: , : , :
35	instantiation	60	⊢
	: , :
36	instantiation	60	⊢
	: , :
37	instantiation	43, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
39	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
40	instantiation	75, 68, 46	⊢
	: , : , :
41	instantiation	47, 48	⊢
	:
42	instantiation	75, 49, 50	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	51, 77, 52, 53, 54, 55	⊢
	: , : , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
46	instantiation	75, 71, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
50	instantiation	57, 58, 59	⊢
	: , :
51	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
52	instantiation	60	⊢
	: , :
53	instantiation	60	⊢
	: , :
54	instantiation	61, 63	⊢
	:
55	instantiation	62, 63	⊢
	:
56	instantiation	75, 73, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
58	instantiation	75, 66, 65	⊢
	: , : , :
59	instantiation	75, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
62	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
63	instantiation	75, 68, 69	⊢
	: , : , :
64	instantiation	75, 76, 70	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
67	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
69	instantiation	75, 71, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	75, 73, 74	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
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.nat2
^*equality replacement requirements