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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	12, 4	, , ⊢
	: , :
3	instantiation	5, 6, 7	, , ⊢
	: , : , :
4	instantiation	8, 27, 29, 9^*	, , ⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	10, 11	, ⊢
	: , : , :
7	instantiation	12, 13	, , ⊢
	: , :
8	theorem		⊢
	proveit.numbers.division.frac_cancel_left
9	instantiation	14, 37, 44, 15^, 16^	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	17, 37, 29	, ⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	18, 29, 37, 19, 20, 21^, 22^	, , ⊢
	: , : , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
15	instantiation	23, 37	⊢
	:
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
17	theorem		⊢
	proveit.numbers.multiplication.commutation
18	theorem		⊢
	proveit.numbers.division.prod_of_fracs
19	instantiation	49, 24, 25	⊢
	: , : , :
20	instantiation	26, 27, 38	, ⊢
	: , :
21	instantiation	28, 29	⊢
	:
22	instantiation	30, 31	⊢
	:
23	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
25	instantiation	49, 32, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
27	instantiation	34, 37, 35	, ⊢
	:
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
31	instantiation	36, 37, 38	⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33	instantiation	49, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
37	assumption		⊢
38	instantiation	49, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
40	instantiation	49, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	49, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	49, 47, 48	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements