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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	3, 14, 4, 5, 6, 7^, 8^	⊢
	: , : , : , :
3	theorem		⊢
	proveit.numbers.division.prod_of_fracs
4	instantiation	55, 45, 9	⊢
	: , : , :
5	instantiation	55, 11, 10	⊢
	: , : , :
6	instantiation	55, 11, 12	⊢
	: , : , :
7	instantiation	13, 14	⊢
	:
8	instantiation	15, 16	⊢
	:
9	instantiation	55, 49, 17	⊢
	: , : , :
10	instantiation	55, 19, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
12	instantiation	55, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.division.frac_one_denom
14	instantiation	21, 22, 23	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
16	instantiation	55, 45, 24	⊢
	: , : , :
17	instantiation	55, 53, 25	⊢
	: , : , :
18	instantiation	55, 27, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
20	instantiation	55, 27, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	39, 29, 35	⊢
	: , :
23	instantiation	30, 31, 57, 32, 33, 34, 40, 41, 35	⊢
	: , : , : , : , : , :
24	instantiation	55, 49, 36	⊢
	: , : , :
25	assumption		⊢
26	instantiation	55, 38, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
28	instantiation	55, 38, 48	⊢
	: , : , :
29	instantiation	39, 40, 41	⊢
	: , :
30	theorem		⊢
	proveit.numbers.multiplication.disassociation
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
33	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34	instantiation	42	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
36	instantiation	55, 53, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
40	instantiation	55, 45, 44	⊢
	: , : , :
41	instantiation	55, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	instantiation	55, 47, 48	⊢
	: , : , :
44	instantiation	55, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	instantiation	55, 51, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
48	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	55, 53, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	55, 56, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements