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