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.multiplication.distribute_through_subtract
2	reference	34	⊢
3	reference	59	⊢
4	reference	36	⊢
5	reference	38	⊢
6	reference	22	⊢
7	reference	11	, ⊢
8	instantiation	10, 11	, ⊢
	:
9	instantiation	12, 22, 13, 14, 15^, 16^	, ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
11	instantiation	17, 22, 18	, ⊢
	: , :
12	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
14	instantiation	19, 59, 34, 36, 52, 20	⊢
	: , : , : , : , :
15	instantiation	21, 22	⊢
	:
16	instantiation	28, 23, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
18	instantiation	57, 44, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
20	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
21	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
22	assumption		⊢
23	instantiation	26, 59, 35, 34, 27, 36, 38, 39	⊢
	: , : , : , : , : , :
24	instantiation	28, 29, 30	⊢
	: , : , :
25	instantiation	57, 48, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.disassociation
27	instantiation	42	⊢
	: , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	32, 59, 34, 36, 38, 39	⊢
	: , : , : , : , : , : , :
30	instantiation	33, 34, 35, 59, 36, 37, 38, 39, 40^*	⊢
	: , : , : , : , : , :
31	instantiation	57, 53, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.addition.leftward_commutation
33	theorem		⊢
	proveit.numbers.addition.association
34	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
36	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37	instantiation	42	⊢
	: , :
38	instantiation	57, 44, 43	⊢
	: , : , :
39	instantiation	57, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
41	instantiation	46, 47, 54	⊢
	: , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	instantiation	57, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	50, 51, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
47	instantiation	57, 58, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	57, 53, 54	⊢
	: , : , :
50	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
51	instantiation	55, 56	⊢
	: , :
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	57, 58, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements