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	23	⊢
3	reference	35	⊢
4	instantiation	57, 31, 8	⊢
	: , : , :
5	instantiation	57, 31, 9	⊢
	: , : , :
6	instantiation	10, 35	⊢
	:
7	instantiation	11, 12, 13	⊢
	: , : , :
8	instantiation	57, 39, 14	⊢
	: , : , :
9	instantiation	57, 39, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.division.frac_one_denom
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	16, 59, 17, 18, 19, 20	⊢
	: , : , : , :
13	instantiation	21, 22, 23, 24^, 25^	⊢
	: , : , :
14	instantiation	57, 45, 26	⊢
	: , : , :
15	instantiation	57, 45, 27	⊢
	: , : , :
16	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
17	instantiation	28	⊢
	: , :
18	instantiation	28	⊢
	: , :
19	instantiation	29, 35	⊢
	:
20	instantiation	34, 30	⊢
	:
21	theorem		⊢
	proveit.numbers.division.frac_cancel_left
22	instantiation	57, 31, 32	⊢
	: , : , :
23	instantiation	57, 42, 33	⊢
	: , : , :
24	instantiation	34, 35	⊢
	:
25	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
26	instantiation	57, 51, 36	⊢
	: , : , :
27	instantiation	57, 51, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
30	instantiation	57, 42, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32	instantiation	57, 39, 40	⊢
	: , : , :
33	instantiation	57, 48, 41	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
35	instantiation	57, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
38	instantiation	57, 48, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40	instantiation	57, 45, 46	⊢
	: , : , :
41	instantiation	57, 54, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	57, 48, 49	⊢
	: , : , :
44	instantiation	57, 54, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46	instantiation	57, 51, 52	⊢
	: , : , :
47	instantiation	57, 58, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	57, 54, 55	⊢
	: , : , :
50	instantiation	57, 58, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	57, 58, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements