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	⊢
	:
1	theorem		⊢
	proveit.numbers.division.frac_one_denom
2	instantiation	9, 3, 4	⊢
	: , : , :
3	instantiation	25, 12, 5	⊢
	: , :
4	instantiation	6, 7, 8	⊢
	: , : , :
5	instantiation	9, 10, 11	⊢
	: , : , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	17, 57, 13, 18, 15, 19, 12, 26, 27, 21	⊢
	: , : , : , : , : , :
8	instantiation	17, 18, 42, 13, 19, 14, 15, 22, 23, 26, 27, 21	⊢
	: , : , : , : , : , :
9	theorem		⊢
	proveit.logic.equality.sub_right_side_into
10	instantiation	25, 16, 21	⊢
	: , :
11	instantiation	17, 18, 42, 57, 19, 20, 26, 27, 21	⊢
	: , : , : , : , : , :
12	instantiation	25, 22, 23	⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
14	instantiation	28	⊢
	: , :
15	instantiation	24	⊢
	: , : , :
16	instantiation	25, 26, 27	⊢
	: , :
17	theorem		⊢
	proveit.numbers.multiplication.disassociation
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	28	⊢
	: , :
21	instantiation	55, 32, 29	⊢
	: , : , :
22	instantiation	55, 32, 30	⊢
	: , : , :
23	instantiation	55, 32, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
25	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
27	instantiation	55, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
30	instantiation	55, 37, 34	⊢
	: , : , :
31	instantiation	55, 35, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	55, 37, 38	⊢
	: , : , :
34	instantiation	55, 40, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	55, 40, 41	⊢
	: , : , :
39	instantiation	55, 56, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	55, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
43	instantiation	45, 46, 47	⊢
	: , :
44	assumption		⊢
45	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
46	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
47	instantiation	48, 49, 50	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
49	instantiation	55, 51, 52	⊢
	: , : , :
50	instantiation	53, 54	⊢
	:
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
52	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
53	theorem		⊢
	proveit.numbers.negation.int_closure
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1