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^*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
2	reference	43	⊢
3	reference	56	⊢
4	instantiation	17, 5, 6	⊢
	: , : , :
5	instantiation	25, 26, 7, 8, 9, 10	⊢
	: , : , : , :
6	instantiation	11, 12, 13, 14, 15^, 16^	⊢
	: , : , :
7	instantiation	36	⊢
	: , :
8	instantiation	36	⊢
	: , :
9	instantiation	17, 18, 19	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_4
11	theorem		⊢
	proveit.numbers.division.frac_cancel_left
12	instantiation	57, 21, 20	⊢
	: , : , :
13	instantiation	57, 21, 22	⊢
	: , : , :
14	instantiation	57, 45, 23	⊢
	: , : , :
15	instantiation	38, 24	⊢
	:
16	theorem		⊢
	proveit.numbers.numerals.decimals.mult_8_2
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	25, 26, 27, 28, 29, 30	⊢
	: , : , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_4
20	instantiation	57, 32, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22	instantiation	57, 32, 33	⊢
	: , : , :
23	instantiation	57, 52, 34	⊢
	: , : , :
24	instantiation	57, 45, 35	⊢
	: , : , :
25	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
27	instantiation	36	⊢
	: , :
28	instantiation	36	⊢
	: , :
29	instantiation	37, 39	⊢
	:
30	instantiation	38, 39	⊢
	:
31	instantiation	57, 41, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33	instantiation	57, 41, 42	⊢
	: , : , :
34	instantiation	57, 55, 43	⊢
	: , : , :
35	instantiation	57, 52, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
39	instantiation	57, 45, 46	⊢
	: , : , :
40	instantiation	57, 48, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
42	instantiation	57, 48, 49	⊢
	: , : , :
43	instantiation	57, 58, 50	⊢
	: , : , :
44	instantiation	57, 55, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	instantiation	57, 52, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat8
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	instantiation	57, 58, 54	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	57, 55, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	57, 58, 59	⊢
	: , : , :
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.nat4
^*equality replacement requirements