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	13	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 32, 7, 25, 24, 8^*	⊢
	: , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	9, 24, 10, 11^*	⊢
	: , :
6	theorem		⊢
	proveit.numbers.division.prod_of_fracs
7	instantiation	56, 38, 12	⊢
	: , : , :
8	instantiation	13, 14, 15	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
11	instantiation	16, 26	⊢
	:
12	instantiation	56, 44, 17	⊢
	: , : , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	18, 55, 19, 20, 21, 22	⊢
	: , : , : , :
15	instantiation	23, 24, 25, 26, 27^, 28^	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
17	instantiation	56, 50, 29	⊢
	: , : , :
18	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
19	instantiation	30	⊢
	: , :
20	instantiation	30	⊢
	: , :
21	instantiation	31, 32	⊢
	:
22	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_2
23	theorem		⊢
	proveit.numbers.division.frac_cancel_left
24	instantiation	56, 34, 33	⊢
	: , : , :
25	instantiation	56, 34, 35	⊢
	: , : , :
26	instantiation	56, 38, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
28	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_3
29	instantiation	56, 57, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
32	instantiation	56, 38, 39	⊢
	: , : , :
33	instantiation	56, 41, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
35	instantiation	56, 41, 42	⊢
	: , : , :
36	instantiation	56, 44, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	56, 44, 45	⊢
	: , : , :
40	instantiation	56, 47, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
42	instantiation	56, 47, 48	⊢
	: , : , :
43	instantiation	56, 50, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	56, 50, 51	⊢
	: , : , :
46	instantiation	56, 53, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
48	instantiation	56, 53, 54	⊢
	: , : , :
49	instantiation	56, 57, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	56, 57, 58	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements