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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 11, 7, 55, 13, 8, 15, 16, 17, 18, 14, 19	⊢
	: , : , : , : , : , : , :
5	instantiation	9, 55, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
8	instantiation	20	⊢
	: , : , : , :
9	theorem		⊢
	proveit.numbers.multiplication.association
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	21	⊢
	: , : , : , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	53, 26, 22	⊢
	: , : , :
15	instantiation	53, 26, 23	⊢
	: , : , :
16	instantiation	53, 26, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
18	instantiation	53, 26, 25	⊢
	: , : , :
19	instantiation	53, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
22	instantiation	28, 29, 50	⊢
	: , : , :
23	instantiation	53, 33, 30	⊢
	: , : , :
24	instantiation	53, 31, 32	⊢
	: , : , :
25	instantiation	53, 33, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
27	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
28	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
29	instantiation	35, 36	⊢
	: , :
30	instantiation	53, 38, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	53, 38, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
37	instantiation	53, 54, 40	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	53, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	instantiation	43, 44, 45	⊢
	: , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
44	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
45	instantiation	46, 47, 48	⊢
	: , :
46	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
47	instantiation	53, 49, 50	⊢
	: , : , :
48	instantiation	51, 52	⊢
	:
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
50	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
51	theorem		⊢
	proveit.numbers.negation.int_closure
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1