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, 4^, 5^	⊢
	: , :
1	theorem		⊢
	proveit.trigonometry.complex_unit_circle_chord_length
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
3	instantiation	6, 7, 8	⊢
	: , : , :
4	instantiation	23, 9, 10	⊢
	: , : , :
5	instantiation	11, 12	⊢
	: , :
6	theorem		⊢
	proveit.logic.equality.sub_right_side_into
7	instantiation	20, 13, 44	⊢
	: , :
8	instantiation	14, 32, 53, 30, 34, 28, 36, 37, 38	⊢
	: , : , : , : , : , :
9	instantiation	18, 15	⊢
	: , : , :
10	instantiation	16, 17	⊢
	:
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	18, 19	⊢
	: , : , :
13	instantiation	20, 41, 42	⊢
	: , :
14	theorem		⊢
	proveit.numbers.multiplication.disassociation
15	instantiation	21, 35	⊢
	:
16	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
17	instantiation	51, 43, 22	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.substitution
19	instantiation	23, 24, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
21	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
22	instantiation	51, 47, 26	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	27, 32, 53, 30, 34, 28, 36, 37, 35, 38	⊢
	: , : , : , : , : , : , :
25	instantiation	29, 30, 31, 32, 33, 34, 35, 36, 37, 38	⊢
	: , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
27	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
28	instantiation	39	⊢
	: , :
29	theorem		⊢
	proveit.numbers.multiplication.association
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
32	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
33	instantiation	40	⊢
	: , : , :
34	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
36	instantiation	51, 43, 41	⊢
	: , : , :
37	instantiation	51, 43, 42	⊢
	: , : , :
38	instantiation	51, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
41	instantiation	51, 45, 46	⊢
	: , : , :
42	instantiation	51, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	assumption		⊢
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	51, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	51, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements