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^*	⊢
	:
1	theorem		⊢
	proveit.numbers.absolute_value.abs_even
2	instantiation	42, 33, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 23, 24, 25, 8^, 9^	⊢
	: , :
4	instantiation	10, 11, 12	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
7	instantiation	13	⊢
	: , : , :
8	instantiation	15, 14	⊢
	:
9	instantiation	15, 16	⊢
	:
10	theorem		⊢
	proveit.logic.equality.sub_right_side_into
11	instantiation	29, 17, 34	⊢
	: , :
12	instantiation	18, 19, 44, 20, 21, 22, 23, 24, 25	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
14	instantiation	26, 44	⊢
	:
15	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
16	instantiation	27, 28	⊢
	: , :
17	instantiation	29, 31, 32	⊢
	: , :
18	theorem		⊢
	proveit.numbers.multiplication.disassociation
19	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	30	⊢
	: , :
23	instantiation	42, 33, 31	⊢
	: , : , :
24	instantiation	42, 33, 32	⊢
	: , : , :
25	instantiation	42, 33, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
27	theorem		⊢
	proveit.numbers.ordering.relax_less
28	instantiation	35, 39	⊢
	:
29	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	instantiation	42, 36, 37	⊢
	: , : , :
32	instantiation	42, 38, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	42, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements