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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
2	instantiation	5, 6, 39, 7	⊢
	: , :
3	reference	6	⊢
4	instantiation	8, 22, 47, 9^*	⊢
	: , : , : , :
5	theorem		⊢
	proveit.numbers.division.div_complex_closure
6	instantiation	48, 41, 10	⊢
	: , : , :
7	instantiation	27, 11	⊢
	:
8	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
9	instantiation	23, 12, 13	⊢
	: , : , :
10	instantiation	48, 44, 14	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
12	instantiation	30, 50, 15, 16, 17, 18	⊢
	: , : , : , :
13	instantiation	19, 20, 21	⊢
	:
14	instantiation	48, 46, 22	⊢
	: , : , :
15	instantiation	36	⊢
	: , :
16	instantiation	36	⊢
	: , :
17	instantiation	23, 24, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
19	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
20	instantiation	48, 41, 26	⊢
	: , : , :
21	instantiation	27, 28	⊢
	:
22	instantiation	48, 49, 29	⊢
	: , : , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	30, 50, 31, 32, 33, 34	⊢
	: , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
26	instantiation	48, 44, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
30	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
31	instantiation	36	⊢
	: , :
32	instantiation	36	⊢
	: , :
33	instantiation	37, 39	⊢
	:
34	instantiation	38, 39	⊢
	:
35	instantiation	48, 46, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
39	instantiation	48, 41, 42	⊢
	: , : , :
40	instantiation	48, 49, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	48, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	48, 46, 47	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	48, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements