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	, , , ⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 5, 6	, ⊢
	: , : , :
3	instantiation	7, 8, 9, 23, 10^, 11^	, , ⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	12, 13, 66, 14, 15^*	⊢
	: , : , : , :
6	assumption		⊢
7	theorem		⊢
	proveit.numbers.division.frac_cancel_left
8	instantiation	16, 21, 17	, ⊢
	:
9	instantiation	76, 18, 19	⊢
	: , : , :
10	instantiation	20, 21	⊢
	:
11	instantiation	22, 23	, ⊢
	:
12	axiom		⊢
	proveit.numbers.summation.sum_split_last
13	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
14	instantiation	24, 25	⊢
	:
15	instantiation	26, 27, 28	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
17	instantiation	29, 30	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19	instantiation	76, 31, 32	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
21	instantiation	33, 56, 34	⊢
	: , :
22	theorem		⊢
	proveit.numbers.division.frac_one_denom
23	instantiation	35, 52, 36	, ⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
25	instantiation	37, 78, 40, 42, 75, 38	⊢
	: , : , : , : , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	39, 40, 41, 78, 42, 43, 46, 56, 44	⊢
	: , : , : , : , : , :
28	instantiation	45, 56, 46, 47	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
30	instantiation	48, 49	⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
32	instantiation	76, 50, 51	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
34	instantiation	55, 52	⊢
	:
35	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
36	instantiation	76, 62, 53	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
38	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
39	theorem		⊢
	proveit.numbers.addition.disassociation
40	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
43	instantiation	54	⊢
	: , :
44	instantiation	55, 56	⊢
	:
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
46	instantiation	76, 62, 57	⊢
	: , : , :
47	instantiation	58	⊢
	:
48	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
51	instantiation	76, 59, 60	⊢
	: , : , :
52	assumption		⊢
53	instantiation	76, 67, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
55	theorem		⊢
	proveit.numbers.negation.complex_closure
56	instantiation	76, 62, 63	⊢
	: , : , :
57	instantiation	64, 65, 75	⊢
	: , : , :
58	axiom		⊢
	proveit.logic.equality.equals_reflexivity
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
61	instantiation	76, 73, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	76, 67, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
65	instantiation	69, 70	⊢
	: , :
66	instantiation	71, 72, 74	⊢
	: , :
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	76, 73, 74	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
71	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
72	instantiation	76, 77, 75	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
74	instantiation	76, 77, 78	⊢
	: , : , :
75	assumption		⊢
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements