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