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	, ⊢
	: , :
1	instantiation	5, 6	⊢
	:
2	instantiation	44, 34, 7	⊢
	: , : , :
3	instantiation	8, 9, 10	⊢
	: , : , :
4	instantiation	11, 12	⊢
	:
5	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_exp
6	assumption		⊢
7	instantiation	44, 39, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_right_side_into
9	instantiation	28, 20, 13	⊢
	: , :
10	instantiation	14, 15, 16	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
12	instantiation	44, 17, 18	⊢
	: , : , :
13	instantiation	28, 26, 27	⊢
	: , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	21, 19, 46, 22, 25, 23, 20, 26, 27	⊢
	: , : , : , : , : , :
16	instantiation	21, 22, 46, 23, 24, 25, 29, 30, 26, 27	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
20	instantiation	28, 29, 30	⊢
	: , :
21	theorem		⊢
	proveit.numbers.multiplication.disassociation
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	31	⊢
	: , :
25	instantiation	31	⊢
	: , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
27	instantiation	44, 34, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
29	instantiation	44, 34, 33	⊢
	: , : , :
30	instantiation	44, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32	instantiation	44, 37, 36	⊢
	: , : , :
33	instantiation	44, 37, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	44, 39, 40	⊢
	: , : , :
36	instantiation	44, 42, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	44, 42, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
41	assumption		⊢
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	44, 45, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2