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