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	reference	52	⊢
2	instantiation	19, 4	⊢
	: , : , :
3	instantiation	5, 6, 7^*	⊢
	: , :
4	instantiation	8, 22, 73, 41, 9^*	⊢
	: , :
5	theorem		⊢
	proveit.logic.equality.equals_reversal
6	instantiation	10, 11, 84, 69, 12, 13, 23, 22	⊢
	: , : , : , : , : , :
7	instantiation	52, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.division.div_as_mult
9	instantiation	52, 16, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	70	⊢
	: , :
14	instantiation	19, 18	⊢
	: , : , :
15	instantiation	71, 22	⊢
	:
16	instantiation	19, 20	⊢
	: , : , :
17	instantiation	21, 22, 23	⊢
	: , :
18	instantiation	24, 60, 81, 25^*	⊢
	: , : , : , :
19	axiom		⊢
	proveit.logic.equality.substitution
20	instantiation	26, 27, 28, 29^*	⊢
	: , :
21	theorem		⊢
	proveit.numbers.multiplication.commutation
22	instantiation	82, 75, 30	⊢
	: , : , :
23	instantiation	82, 75, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
25	instantiation	52, 32, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
27	instantiation	82, 34, 35	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
29	instantiation	36, 73	⊢
	:
30	instantiation	82, 37, 38	⊢
	: , : , :
31	instantiation	39, 40, 76, 41	⊢
	: , :
32	instantiation	61, 84, 42, 43, 44, 45	⊢
	: , : , : , :
33	instantiation	46, 47, 48	⊢
	:
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
35	instantiation	82, 49, 50	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
39	theorem		⊢
	proveit.numbers.division.div_real_closure
40	instantiation	82, 78, 51	⊢
	: , : , :
41	instantiation	56, 68	⊢
	:
42	instantiation	70	⊢
	: , :
43	instantiation	70	⊢
	: , :
44	instantiation	52, 53, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
46	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
47	instantiation	82, 75, 55	⊢
	: , : , :
48	instantiation	56, 57	⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
50	instantiation	82, 58, 59	⊢
	: , : , :
51	instantiation	82, 80, 60	⊢
	: , : , :
52	axiom		⊢
	proveit.logic.equality.equals_transitivity
53	instantiation	61, 84, 62, 63, 64, 65	⊢
	: , : , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
55	instantiation	82, 78, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
59	instantiation	82, 67, 68	⊢
	: , : , :
60	instantiation	82, 83, 69	⊢
	: , : , :
61	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
62	instantiation	70	⊢
	: , :
63	instantiation	70	⊢
	: , :
64	instantiation	71, 73	⊢
	:
65	instantiation	72, 73	⊢
	:
66	instantiation	82, 80, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
70	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
71	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
72	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
73	instantiation	82, 75, 76	⊢
	: , : , :
74	instantiation	82, 83, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
76	instantiation	82, 78, 79	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	82, 80, 81	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
81	instantiation	82, 83, 84	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements