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.numbers.number_sets.complex_numbers.unit_length_complex_polar_negation
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8	⊢
	: , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	13, 9, 34	⊢
	: , :
6	instantiation	10, 22, 43, 20, 24, 18, 26, 27, 28	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	11, 12	⊢
	: , : , :
9	instantiation	13, 31, 32	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.disassociation
11	axiom		⊢
	proveit.logic.equality.substitution
12	instantiation	14, 15, 16	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	17, 22, 43, 20, 24, 18, 26, 27, 25, 28	⊢
	: , : , : , : , : , : , :
16	instantiation	19, 20, 21, 22, 23, 24, 25, 26, 27, 28	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
18	instantiation	29	⊢
	: , :
19	theorem		⊢
	proveit.numbers.multiplication.association
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	instantiation	30	⊢
	: , : , :
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
26	instantiation	41, 33, 31	⊢
	: , : , :
27	instantiation	41, 33, 32	⊢
	: , : , :
28	instantiation	41, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
31	instantiation	41, 35, 36	⊢
	: , : , :
32	instantiation	41, 37, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	41, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	41, 42, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements