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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 5, 6, 7, 8	⊢
	: , : , : , : , :
3	instantiation	24, 9, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
5	instantiation	71, 55, 11	⊢
	: , : , :
6	instantiation	71, 55, 12	⊢
	: , : , :
7	instantiation	71, 14, 13	⊢
	: , : , :
8	instantiation	71, 14, 15	⊢
	: , : , :
9	instantiation	34, 16	⊢
	: , : , :
10	instantiation	34, 17	⊢
	: , : , :
11	instantiation	71, 59, 18	⊢
	: , : , :
12	instantiation	71, 59, 19	⊢
	: , : , :
13	instantiation	71, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
15	instantiation	71, 22, 23	⊢
	: , : , :
16	instantiation	24, 25, 26	⊢
	: , : , :
17	instantiation	34, 27	⊢
	: , : , :
18	instantiation	71, 63, 62	⊢
	: , : , :
19	instantiation	71, 63, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
21	instantiation	29, 30, 31	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
23	instantiation	71, 32, 33	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	34, 35	⊢
	: , : , :
26	instantiation	36, 47	⊢
	:
27	instantiation	37, 47	⊢
	:
28	instantiation	71, 38, 39	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
30	instantiation	71, 40, 41	⊢
	: , : , :
31	instantiation	42, 43, 73	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33	instantiation	71, 44, 45	⊢
	: , : , :
34	axiom		⊢
	proveit.logic.equality.substitution
35	instantiation	46, 47	⊢
	:
36	theorem		⊢
	proveit.numbers.division.frac_one_denom
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
38	instantiation	48, 49, 50	⊢
	: , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
41	instantiation	71, 51, 52	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
43	instantiation	53, 54	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
47	instantiation	71, 55, 56	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
49	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
50	instantiation	57, 64, 58	⊢
	: , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	71, 59, 60	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
58	instantiation	61, 62	⊢
	:
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	71, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.negation.int_closure
62	instantiation	71, 69, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	66, 67, 68	⊢
	: , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
66	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
67	instantiation	71, 69, 70	⊢
	: , : , :
68	instantiation	71, 72, 73	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
73	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos