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	reference	31	⊢
2	instantiation	31, 4, 5	, , ⊢
	: , : , :
3	instantiation	6, 65, 39, 38, 7, 40, 8, 9, 27	, , ⊢
	: , : , : , : , : , :
4	instantiation	31, 10, 11	, , ⊢
	: , : , :
5	instantiation	15, 12	, ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.disassociation
7	instantiation	49	⊢
	: , :
8	instantiation	13, 23, 44	, ⊢
	: , :
9	instantiation	13, 27, 14	, ⊢
	: , :
10	instantiation	15, 16	, ⊢
	: , : , :
11	instantiation	17, 23, 27, 58	, , ⊢
	: , : , :
12	instantiation	18, 46, 52, 21, 56, 19, 20^*	, ⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
14	instantiation	63, 55, 21	⊢
	: , : , :
15	axiom		⊢
	proveit.logic.equality.substitution
16	instantiation	22, 27, 23	, ⊢
	: , :
17	theorem		⊢
	proveit.numbers.exponentiation.pos_power_of_product
18	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
19	instantiation	24, 25	⊢
	: , :
20	instantiation	26, 27	⊢
	:
21	instantiation	28, 52, 29	⊢
	: , :
22	theorem		⊢
	proveit.numbers.multiplication.commutation
23	instantiation	63, 55, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.equals_reversal
25	instantiation	31, 32, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27	instantiation	63, 55, 34	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	instantiation	63, 59, 35	⊢
	: , : , :
30	instantiation	63, 59, 36	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	37, 38, 39, 65, 40, 41, 44, 42, 51	⊢
	: , : , : , : , : , :
33	instantiation	43, 51, 44, 45	⊢
	: , : , :
34	instantiation	63, 57, 46	⊢
	: , : , :
35	instantiation	63, 61, 47	⊢
	: , : , :
36	instantiation	63, 61, 48	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.disassociation
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	49	⊢
	: , :
42	instantiation	50, 51	⊢
	:
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
44	instantiation	63, 55, 52	⊢
	: , : , :
45	instantiation	53	⊢
	:
46	assumption		⊢
47	instantiation	54, 62	⊢
	:
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	theorem		⊢
	proveit.numbers.negation.complex_closure
51	instantiation	63, 55, 56	⊢
	: , : , :
52	instantiation	63, 57, 58	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	theorem		⊢
	proveit.numbers.negation.int_closure
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	63, 59, 60	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
58	assumption		⊢
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	63, 61, 62	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements