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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9^*	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	10, 15, 12, 13	⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
7	instantiation	11, 15, 12, 13	⊢
	: , :
8	instantiation	11, 16, 12, 13	⊢
	: , :
9	instantiation	14, 15, 16, 17, 18^, 19^	⊢
	: , : , : , :
10	theorem		⊢
	proveit.numbers.division.neg_frac_neg_numerator
11	theorem		⊢
	proveit.numbers.division.div_complex_closure
12	instantiation	43, 23, 20	⊢
	: , : , :
13	instantiation	21, 45	⊢
	:
14	theorem		⊢
	proveit.numbers.division.prod_of_fracs
15	instantiation	43, 23, 22	⊢
	: , : , :
16	instantiation	43, 23, 24	⊢
	: , : , :
17	instantiation	43, 25, 26	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_5
19	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
20	instantiation	43, 29, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
22	instantiation	43, 29, 28	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	43, 29, 30	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
26	instantiation	43, 31, 32	⊢
	: , : , :
27	instantiation	43, 35, 33	⊢
	: , : , :
28	instantiation	43, 35, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	43, 35, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
32	instantiation	43, 37, 38	⊢
	: , : , :
33	instantiation	43, 41, 39	⊢
	: , : , :
34	instantiation	43, 41, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
36	instantiation	43, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	43, 44, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
^*equality replacement requirements