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, 45, 5, 6, 7, 8	⊢
	: , : , : , :
3	instantiation	9, 10, 11, 23, 12^, 13^, 14^*	⊢
	: , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	instantiation	15	⊢
	: , :
6	instantiation	15	⊢
	: , :
7	instantiation	21, 16	⊢
	:
8	instantiation	17, 23	⊢
	:
9	theorem		⊢
	proveit.numbers.division.frac_cancel_left
10	instantiation	43, 19, 18	⊢
	: , : , :
11	instantiation	43, 19, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
13	instantiation	21, 23	⊢
	:
14	instantiation	22, 23	⊢
	:
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	instantiation	43, 28, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
18	instantiation	43, 26, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20	instantiation	43, 26, 27	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
22	theorem		⊢
	proveit.numbers.division.frac_one_denom
23	instantiation	43, 28, 29	⊢
	: , : , :
24	instantiation	43, 34, 30	⊢
	: , : , :
25	instantiation	43, 32, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27	instantiation	43, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
29	instantiation	43, 34, 35	⊢
	: , : , :
30	instantiation	43, 40, 36	⊢
	: , : , :
31	instantiation	43, 38, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33	instantiation	43, 38, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	43, 40, 41	⊢
	: , : , :
36	instantiation	43, 44, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	43, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements