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