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^*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
2	instantiation	56, 57, 6	⊢
	: , : , :
3	reference	55	⊢
4	instantiation	56, 57, 7	⊢
	: , : , :
5	instantiation	20, 8, 9	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
8	instantiation	29, 58, 10, 11, 12, 13	⊢
	: , : , : , :
9	instantiation	14, 15, 16, 40, 17^, 18^, 19^*	⊢
	: , : , :
10	instantiation	38	⊢
	: , :
11	instantiation	38	⊢
	: , :
12	instantiation	20, 21, 22	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
14	theorem		⊢
	proveit.numbers.division.frac_cancel_left
15	instantiation	56, 24, 23	⊢
	: , : , :
16	instantiation	56, 24, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.mult_4_2
18	instantiation	26, 27	⊢
	:
19	instantiation	28, 40	⊢
	:
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	29, 58, 30, 31, 32, 33	⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_6
23	instantiation	56, 35, 34	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
25	instantiation	56, 35, 36	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
27	instantiation	56, 45, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
30	instantiation	38	⊢
	: , :
31	instantiation	38	⊢
	: , :
32	instantiation	39, 40	⊢
	:
33	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_3
34	instantiation	56, 42, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
36	instantiation	56, 42, 43	⊢
	: , : , :
37	instantiation	56, 51, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
40	instantiation	56, 45, 46	⊢
	: , : , :
41	instantiation	56, 48, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43	instantiation	56, 48, 49	⊢
	: , : , :
44	instantiation	56, 54, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	instantiation	56, 51, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
50	instantiation	56, 57, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	56, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	56, 57, 58	⊢
	: , : , :
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.nat2
^*equality replacement requirements