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