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	⊢
	: , : , :
1	reference	27	⊢
2	instantiation	3, 4, 5	⊢
	: , : , :
3	theorem		⊢
	proveit.logic.equality.sub_right_side_into
4	instantiation	6, 25, 7, 8^, 9^	⊢
	: , :
5	instantiation	10, 11	⊢
	:
6	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.complex_polar_negation
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
8	instantiation	12, 21	⊢
	:
9	instantiation	22, 13, 14	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
11	instantiation	15, 30, 16	⊢
	: , :
12	theorem		⊢
	proveit.numbers.addition.elim_zero_left
13	instantiation	27, 17	⊢
	: , : , :
14	instantiation	18, 19	⊢
	:
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	20, 35, 21	⊢
	: , :
17	instantiation	22, 23, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
19	instantiation	42, 36, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
21	instantiation	42, 36, 26	⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	27, 28	⊢
	: , : , :
24	instantiation	29, 30	⊢
	:
25	instantiation	42, 31, 32	⊢
	: , : , :
26	instantiation	42, 40, 33	⊢
	: , : , :
27	axiom		⊢
	proveit.logic.equality.substitution
28	instantiation	34, 35	⊢
	:
29	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
30	instantiation	42, 36, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
32	instantiation	42, 38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
34	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	42, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	42, 43, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements