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	16	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	10, 26, 30	⊢
	: , :
6	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
7	instantiation	13, 22, 23, 24, 14, 11, 26, 31, 12, 30	⊢
	: , : , : , : , : , :
8	instantiation	13, 23, 63, 14, 15, 26, 31, 20, 27, 30	⊢
	: , : , : , : , : , :
9	instantiation	16, 17, 18	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
11	instantiation	34	⊢
	: , :
12	instantiation	19, 20, 27	⊢
	: , :
13	theorem		⊢
	proveit.numbers.addition.disassociation
14	instantiation	34	⊢
	: , :
15	instantiation	34	⊢
	: , :
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	21, 22, 63, 23, 24, 25, 26, 31, 27, 30, 28	⊢
	: , : , : , : , : , : , : , :
18	instantiation	29, 30, 31, 32	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
20	instantiation	61, 38, 33	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	34	⊢
	: , :
26	instantiation	61, 38, 35	⊢
	: , : , :
27	instantiation	61, 38, 36	⊢
	: , : , :
28	instantiation	40	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
30	instantiation	61, 38, 37	⊢
	: , : , :
31	instantiation	61, 38, 39	⊢
	: , : , :
32	instantiation	40	⊢
	:
33	instantiation	61, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	instantiation	46, 47, 60	⊢
	: , : , :
36	instantiation	61, 44, 43	⊢
	: , : , :
37	instantiation	61, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	46, 47, 48	⊢
	: , : , :
40	axiom		⊢
	proveit.logic.equality.equals_reflexivity
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
42	instantiation	61, 49, 50	⊢
	: , : , :
43	instantiation	61, 52, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	61, 52, 58	⊢
	: , : , :
46	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
47	instantiation	53, 54	⊢
	: , :
48	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
50	instantiation	61, 55, 56	⊢
	: , : , :
51	instantiation	57, 58	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
56	instantiation	59, 60	⊢
	:
57	theorem		⊢
	proveit.numbers.negation.int_closure
58	instantiation	61, 62, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.negation.int_neg_closure
60	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1