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, 35, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14	⊢
	: , : , : , : , : , :
3	theorem		⊢
	proveit.numbers.multiplication.disassociation
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	15	⊢
	: , : , : , :
7	instantiation	16	⊢
	: , :
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	48, 21, 17	⊢
	: , : , :
10	instantiation	48, 21, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
12	instantiation	48, 21, 19	⊢
	: , : , :
13	instantiation	48, 21, 20	⊢
	: , : , :
14	instantiation	48, 21, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	instantiation	48, 26, 23	⊢
	: , : , :
18	instantiation	48, 24, 25	⊢
	: , : , :
19	instantiation	48, 26, 27	⊢
	: , : , :
20	instantiation	28, 29, 45	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
22	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
23	instantiation	48, 31, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
27	instantiation	48, 31, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
29	instantiation	33, 34	⊢
	: , :
30	instantiation	48, 49, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
32	instantiation	48, 36, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
36	instantiation	38, 39, 40	⊢
	: , :
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
39	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
40	instantiation	41, 42, 43	⊢
	: , :
41	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
42	instantiation	48, 44, 45	⊢
	: , : , :
43	instantiation	46, 47	⊢
	:
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
45	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
46	theorem		⊢
	proveit.numbers.negation.int_closure
47	instantiation	48, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1