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	theorem		⊢
	proveit.numbers.exponentiation.exp_not_eq_zero
2	instantiation	54, 44, 5	⊢
	: , : , :
3	instantiation	6, 7	⊢
	:
4	instantiation	8, 9	⊢
	:
5	instantiation	54, 49, 15	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.negation.complex_closure
7	instantiation	10, 11, 12, 13	⊢
	: , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
9	instantiation	54, 14, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.division.div_complex_closure
11	instantiation	16, 17, 18	⊢
	: , : , :
12	instantiation	54, 44, 19	⊢
	: , : , :
13	instantiation	20, 42	⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	36, 27, 21	⊢
	: , :
18	instantiation	22, 23, 24	⊢
	: , : , :
19	instantiation	54, 47, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
21	instantiation	36, 33, 34	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	28, 26, 56, 29, 32, 30, 27, 33, 34	⊢
	: , : , : , : , : , :
24	instantiation	28, 29, 56, 30, 31, 32, 37, 38, 33, 34	⊢
	: , : , : , : , : , :
25	instantiation	54, 52, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
27	instantiation	36, 37, 38	⊢
	: , :
28	theorem		⊢
	proveit.numbers.multiplication.disassociation
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	39	⊢
	: , :
32	instantiation	39	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
34	instantiation	54, 44, 40	⊢
	: , : , :
35	instantiation	54, 41, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
37	instantiation	54, 44, 43	⊢
	: , : , :
38	instantiation	54, 44, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	54, 47, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
42	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
43	instantiation	54, 47, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	54, 49, 50	⊢
	: , : , :
46	instantiation	54, 52, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	54, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
51	assumption		⊢
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	54, 55, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2