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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	6, 7, 8, 9, 10^*	⊢
	: , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	11, 12, 51, 13, 14, 15, 23, 20, 21	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.division.frac_cancel_left
7	instantiation	49, 17, 16	⊢
	: , : , :
8	instantiation	49, 17, 18	⊢
	: , : , :
9	instantiation	19, 20, 21	⊢
	: , :
10	instantiation	22, 23	⊢
	:
11	theorem		⊢
	proveit.numbers.multiplication.association
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	instantiation	24	⊢
	: , :
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	49, 26, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18	instantiation	49, 26, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
20	instantiation	49, 47, 28	⊢
	: , : , :
21	instantiation	49, 47, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
23	instantiation	49, 47, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	instantiation	49, 32, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27	instantiation	49, 32, 33	⊢
	: , : , :
28	instantiation	49, 34, 35	⊢
	: , : , :
29	instantiation	49, 36, 37	⊢
	: , : , :
30	instantiation	49, 38, 39	⊢
	: , : , :
31	instantiation	49, 41, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33	instantiation	49, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
37	instantiation	43, 44	⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	49, 45, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
43	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
44	instantiation	49, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	49, 50, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	assumption		⊢
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements