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, 4, 5, 6, 7, 8, 9^*	⊢
	: , : , : , : , : , :
1	reference	28	⊢
2	reference	29	⊢
3	reference	16	⊢
4	reference	30	⊢
5	instantiation	21	⊢
	: , : , : , :
6	instantiation	21	⊢
	: , : , : , :
7	reference	23	⊢
8	instantiation	56, 40, 10	⊢
	: , : , :
9	instantiation	11, 12, 13^*	⊢
	: , :
10	instantiation	35, 36, 14	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	15, 29, 16, 58, 30, 17, 33, 23, 18^*	⊢
	: , : , : , : , : , :
13	instantiation	28, 29, 55, 30, 19, 33, 20^*	⊢
	: , : , : , : , : , :
14	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
15	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
17	instantiation	21	⊢
	: , : , : , :
18	instantiation	22, 23	⊢
	:
19	instantiation	38	⊢
	: , :
20	instantiation	42, 24, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
23	instantiation	56, 40, 26	⊢
	: , : , :
24	instantiation	50, 27	⊢
	: , : , :
25	instantiation	28, 29, 55, 58, 30, 31, 32, 33, 34^*	⊢
	: , : , : , : , : , :
26	instantiation	35, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
28	theorem		⊢
	proveit.numbers.addition.association
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	38	⊢
	: , :
32	instantiation	56, 40, 39	⊢
	: , : , :
33	instantiation	56, 40, 41	⊢
	: , : , :
34	instantiation	42, 43, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
36	instantiation	45, 46	⊢
	: , :
37	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	instantiation	56, 48, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	56, 48, 49	⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	50, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
45	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47	instantiation	56, 53, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	56, 53, 54	⊢
	: , : , :
50	axiom		⊢
	proveit.logic.equality.substitution
51	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
52	instantiation	56, 57, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	56, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements