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	reference	16	⊢
2	instantiation	16, 4, 5	⊢
	: , : , :
3	instantiation	6, 7	⊢
	:
4	instantiation	20, 8	⊢
	: , : , :
5	instantiation	20, 9	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.elim_zero_left
7	instantiation	62, 48, 10	⊢
	: , : , :
8	instantiation	11, 24	⊢
	:
9	instantiation	12, 23, 38, 43, 13^*	⊢
	: , :
10	instantiation	14, 15, 30	⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
12	theorem		⊢
	proveit.numbers.division.div_as_mult
13	instantiation	16, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
15	instantiation	62, 54, 19	⊢
	: , : , :
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	20, 21	⊢
	: , : , :
18	instantiation	22, 23, 24	⊢
	: , :
19	instantiation	62, 25, 26	⊢
	: , : , :
20	axiom		⊢
	proveit.logic.equality.substitution
21	instantiation	27, 28, 44, 29^*	⊢
	: , :
22	theorem		⊢
	proveit.numbers.multiplication.commutation
23	instantiation	62, 48, 30	⊢
	: , : , :
24	instantiation	62, 48, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
26	instantiation	32, 33, 34	⊢
	: , :
27	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
28	instantiation	62, 35, 36	⊢
	: , : , :
29	instantiation	37, 38	⊢
	:
30	instantiation	62, 39, 40	⊢
	: , : , :
31	instantiation	41, 42, 49, 43	⊢
	: , :
32	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
33	instantiation	62, 45, 44	⊢
	: , : , :
34	instantiation	62, 45, 58	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
36	instantiation	62, 46, 47	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
38	instantiation	62, 48, 49	⊢
	: , : , :
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	theorem		⊢
	proveit.numbers.division.div_real_closure
42	instantiation	62, 54, 50	⊢
	: , : , :
43	instantiation	51, 58	⊢
	:
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
47	instantiation	62, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	62, 54, 55	⊢
	: , : , :
50	instantiation	62, 59, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
53	instantiation	62, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	62, 59, 60	⊢
	: , : , :
56	instantiation	62, 63, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	62, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements