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, 50, 55, 7, 9, 8, 5, 10, 11	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 55, 8, 9, 10, 11	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
6	theorem		⊢
	proveit.numbers.addition.elim_zero_any
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	12	⊢
	: , :
10	instantiation	13, 14, 15	⊢
	: , :
11	instantiation	53, 43, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
14	instantiation	17, 24, 18, 19	⊢
	: , :
15	instantiation	53, 43, 20	⊢
	: , : , :
16	instantiation	53, 21, 22	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.div_complex_closure
18	instantiation	23, 37, 24	⊢
	: , :
19	instantiation	25, 26, 27	⊢
	: , : , :
20	instantiation	28, 29, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
22	instantiation	53, 31, 32	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
24	instantiation	53, 43, 33	⊢
	: , : , :
25	theorem		⊢
	proveit.logic.equality.sub_left_side_into
26	instantiation	34, 35	⊢
	:
27	instantiation	36, 37	⊢
	:
28	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
29	instantiation	38, 39	⊢
	: , :
30	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
32	instantiation	53, 40, 41	⊢
	: , : , :
33	instantiation	53, 48, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
36	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
37	instantiation	53, 43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
41	instantiation	45, 46	⊢
	:
42	instantiation	53, 51, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	53, 48, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.negation.int_neg_closure
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	instantiation	53, 54, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	53, 51, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
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.nat2