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, 6^, 7^	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	41	⊢
3	instantiation	8, 35, 11	⊢
	: , :
4	instantiation	63, 55, 9	⊢
	: , : , :
5	instantiation	10, 35, 11, 50, 12, 13	⊢
	: , : , :
6	instantiation	31, 14, 15	⊢
	: , : , :
7	instantiation	31, 16, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
9	instantiation	18, 42, 56	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
11	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
12	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
13	instantiation	19, 48	⊢
	:
14	instantiation	22, 20	⊢
	: , : , :
15	instantiation	21, 34	⊢
	:
16	instantiation	22, 23	⊢
	: , : , :
17	instantiation	24, 62, 51, 25^, 26^, 27^*	⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
20	instantiation	28, 29	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.elim_zero_left
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	44, 29	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
25	instantiation	30, 34	⊢
	:
26	instantiation	31, 32, 33	⊢
	: , : , :
27	instantiation	44, 34	⊢
	:
28	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
29	instantiation	63, 49, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.frac_one_denom
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	36, 57, 37, 38, 39, 40	⊢
	: , : , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_4
34	instantiation	63, 49, 41	⊢
	: , : , :
35	instantiation	63, 55, 42	⊢
	: , : , :
36	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
37	instantiation	43	⊢
	: , :
38	instantiation	43	⊢
	: , :
39	instantiation	44, 45	⊢
	:
40	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
41	instantiation	63, 55, 46	⊢
	: , : , :
42	instantiation	63, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
45	instantiation	63, 49, 50	⊢
	: , : , :
46	instantiation	63, 61, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
48	instantiation	52, 53, 54	⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	63, 55, 56	⊢
	: , : , :
51	instantiation	63, 64, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
53	instantiation	63, 59, 58	⊢
	: , : , :
54	instantiation	63, 59, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	63, 61, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements