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	61, 4, 48	⊢
	: , : , :
3	instantiation	19, 5, 6	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
5	instantiation	7, 8	⊢
	: , : , :
6	instantiation	9, 10, 11, 12	⊢
	: , : , : , :
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	13, 29, 39	⊢
	: , :
9	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
10	instantiation	16, 25, 26, 27, 17, 14, 29, 33, 15, 39	⊢
	: , : , : , : , : , :
11	instantiation	16, 26, 63, 17, 18, 29, 33, 23, 30, 39	⊢
	: , : , : , : , : , :
12	instantiation	19, 20, 21	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
14	instantiation	36	⊢
	: , :
15	instantiation	22, 23, 30	⊢
	: , :
16	theorem		⊢
	proveit.numbers.addition.disassociation
17	instantiation	36	⊢
	: , :
18	instantiation	36	⊢
	: , :
19	axiom		⊢
	proveit.logic.equality.equals_transitivity
20	instantiation	24, 25, 63, 26, 27, 28, 29, 33, 30, 39, 31	⊢
	: , : , : , : , : , : , : , :
21	instantiation	32, 39, 33, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
23	instantiation	61, 44, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	36	⊢
	: , :
29	instantiation	61, 44, 37	⊢
	: , : , :
30	instantiation	38, 39	⊢
	:
31	instantiation	41	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
33	instantiation	61, 44, 40	⊢
	: , : , :
34	instantiation	41	⊢
	:
35	instantiation	61, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	instantiation	46, 47, 60	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.negation.complex_closure
39	instantiation	61, 44, 45	⊢
	: , : , :
40	instantiation	46, 47, 48	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.equality.equals_reflexivity
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
43	instantiation	61, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	61, 51, 52	⊢
	: , : , :
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	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	61, 57, 58	⊢
	: , : , :
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.number_sets.rational_numbers.int_within_rational
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