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