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	33	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 20, 9^, 10^	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	11, 12, 58, 63, 40, 13, 14^*	⊢
	: , : , : , :
6	theorem		⊢
	proveit.numbers.division.frac_cancel_left
7	instantiation	76, 16, 15	⊢
	: , : , :
8	instantiation	76, 16, 17	⊢
	: , : , :
9	instantiation	18, 30	⊢
	:
10	instantiation	19, 20	⊢
	:
11	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
12	instantiation	76, 21, 22	⊢
	: , : , :
13	instantiation	23, 24	⊢
	: , :
14	instantiation	25, 30	⊢
	:
15	instantiation	76, 27, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
17	instantiation	76, 27, 28	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
19	theorem		⊢
	proveit.numbers.division.frac_one_denom
20	instantiation	29, 30, 31	⊢
	: , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
22	instantiation	76, 32, 49	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	33, 34, 35	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
26	instantiation	76, 37, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
28	instantiation	76, 37, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
30	instantiation	76, 62, 39	⊢
	: , : , :
31	instantiation	76, 62, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
33	axiom		⊢
	proveit.logic.equality.equals_transitivity
34	instantiation	41, 78, 67, 42, 43, 44, 57, 47, 45	⊢
	: , : , : , : , : , :
35	instantiation	46, 57, 47, 48	⊢
	: , : , :
36	instantiation	76, 50, 49	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	76, 50, 51	⊢
	: , : , :
39	instantiation	76, 69, 52	⊢
	: , : , :
40	instantiation	53, 58, 54	⊢
	: , :
41	theorem		⊢
	proveit.numbers.addition.disassociation
42	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
43	instantiation	55	⊢
	: , :
44	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
45	instantiation	56, 57	⊢
	:
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
47	instantiation	76, 62, 58	⊢
	: , : , :
48	instantiation	59	⊢
	:
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
52	instantiation	76, 74, 60	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
54	instantiation	76, 69, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
56	theorem		⊢
	proveit.numbers.negation.complex_closure
57	instantiation	76, 62, 63	⊢
	: , : , :
58	instantiation	64, 65, 66	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_reflexivity
60	instantiation	76, 77, 67	⊢
	: , : , :
61	instantiation	76, 74, 68	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	76, 69, 70	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
65	instantiation	71, 72	⊢
	: , :
66	assumption		⊢
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	instantiation	73, 75	⊢
	:
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	76, 74, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
73	theorem		⊢
	proveit.numbers.negation.int_closure
74	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements