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.logic.equality.four_chain_transitivity
2	instantiation	23, 5	⊢
	: , : , :
3	instantiation	23, 6	⊢
	: , : , :
4	instantiation	23, 7	⊢
	: , : , :
5	instantiation	15, 8, 9	⊢
	: , : , :
6	instantiation	15, 10, 11	⊢
	: , : , :
7	instantiation	15, 12, 13	⊢
	: , : , :
8	instantiation	23, 22	⊢
	: , : , :
9	instantiation	19, 14	⊢
	:
10	instantiation	15, 16, 17	⊢
	: , : , :
11	instantiation	19, 18	⊢
	:
12	instantiation	23, 22	⊢
	: , : , :
13	instantiation	19, 20	⊢
	:
14	instantiation	26, 21	⊢
	: , :
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	23, 22	⊢
	: , : , :
17	instantiation	23, 24	⊢
	: , : , :
18	instantiation	26, 25	⊢
	: , :
19	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
20	instantiation	26, 27	⊢
	: , :
21	instantiation	28, 29	⊢
	: , :
22	assumption		⊢
23	axiom		⊢
	proveit.logic.equality.substitution
24	instantiation	48, 30, 31	⊢
	: , : , :
25	instantiation	35, 69, 32, 33	⊢
	: , :
26	theorem		⊢
	proveit.logic.equality.unfold_not_equals
27	instantiation	35, 69, 61, 34	⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
29	instantiation	35, 62, 69, 36	⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
31	instantiation	54, 37, 38	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
33	instantiation	39, 60, 40, 41, 42^, 43^	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
35	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
36	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
37	instantiation	67, 59, 44	⊢
	: , : , :
38	instantiation	67, 59, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
41	instantiation	46, 47	⊢
	:
42	instantiation	48, 49, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
44	instantiation	67, 63, 51	⊢
	: , : , :
45	instantiation	67, 63, 52	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
48	theorem		⊢
	proveit.logic.equality.sub_right_side_into
49	instantiation	53, 55	⊢
	:
50	instantiation	54, 55, 56	⊢
	: , :
51	instantiation	67, 65, 57	⊢
	: , : , :
52	instantiation	67, 65, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.elim_zero_right
54	theorem		⊢
	proveit.numbers.addition.commutation
55	instantiation	67, 59, 60	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
57	instantiation	67, 68, 61	⊢
	: , : , :
58	instantiation	67, 68, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
60	instantiation	67, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	67, 65, 66	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	67, 68, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements