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