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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 21, 5, 6, 7^*	⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
4	instantiation	35, 20, 8	⊢
	: , : , :
5	instantiation	9, 23	⊢
	:
6	instantiation	10, 11	⊢
	:
7	instantiation	12, 19, 13, 14^*	⊢
	: , :
8	instantiation	35, 15, 17	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.negation.real_closure
10	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
11	instantiation	35, 16, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
13	instantiation	35, 20, 23	⊢
	: , : , :
14	instantiation	18, 19	⊢
	:
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real_nonzero
17	assumption		⊢
18	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
19	instantiation	35, 20, 21	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
21	instantiation	22, 23, 24, 25	⊢
	: , :
22	theorem		⊢
	proveit.numbers.division.div_real_closure
23	instantiation	35, 27, 26	⊢
	: , : , :
24	instantiation	35, 27, 28	⊢
	: , : , :
25	instantiation	29, 30	⊢
	:
26	instantiation	35, 32, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
28	instantiation	35, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
31	instantiation	35, 36, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
33	instantiation	35, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements