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