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	48	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	48, 6, 7	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	8, 9, 23, 10^*	⊢
	: , :
6	instantiation	11, 63, 78, 14, 12, 15, 21, 17	⊢
	: , : , : , : , : , :
7	instantiation	13, 14, 78, 63, 15, 16, 21, 17, 18^*	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
9	instantiation	76, 69, 19	⊢
	: , : , :
10	instantiation	20, 21	⊢
	:
11	theorem		⊢
	proveit.numbers.addition.disassociation
12	instantiation	64	⊢
	: , :
13	theorem		⊢
	proveit.numbers.addition.association
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	64	⊢
	: , :
17	instantiation	22, 23	⊢
	:
18	instantiation	24, 54, 75, 25^*	⊢
	: , : , : , :
19	instantiation	26, 27	⊢
	:
20	theorem		⊢
	proveit.numbers.negation.double_negation
21	instantiation	76, 69, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.negation.complex_closure
23	instantiation	76, 69, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
25	instantiation	48, 29, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.real_closure
27	instantiation	32, 33, 70, 31	⊢
	: , :
28	instantiation	32, 33, 34, 35	⊢
	: , :
29	instantiation	57, 78, 36, 37, 38, 39	⊢
	: , : , : , :
30	instantiation	40, 41, 42	⊢
	:
31	instantiation	52, 43	⊢
	:
32	theorem		⊢
	proveit.numbers.division.div_real_closure
33	instantiation	76, 72, 44	⊢
	: , : , :
34	instantiation	45, 46, 47	⊢
	: , : , :
35	instantiation	52, 47	⊢
	:
36	instantiation	64	⊢
	: , :
37	instantiation	64	⊢
	: , :
38	instantiation	48, 49, 50	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
40	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
41	instantiation	76, 69, 51	⊢
	: , : , :
42	instantiation	52, 53	⊢
	:
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	instantiation	76, 74, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
46	instantiation	55, 56	⊢
	: , :
47	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
48	axiom		⊢
	proveit.logic.equality.equals_transitivity
49	instantiation	57, 78, 58, 59, 60, 61	⊢
	: , : , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
51	instantiation	76, 72, 62	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
54	instantiation	76, 77, 63	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
57	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
58	instantiation	64	⊢
	: , :
59	instantiation	64	⊢
	: , :
60	instantiation	65, 67	⊢
	:
61	instantiation	66, 67	⊢
	:
62	instantiation	76, 74, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
64	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
65	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
66	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
67	instantiation	76, 69, 70	⊢
	: , : , :
68	instantiation	76, 77, 71	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
70	instantiation	76, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	76, 74, 75	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	76, 77, 78	⊢
	: , : , :
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.nat2
^*equality replacement requirements