Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, c, d
from proveit.logic import And, Equals, InSet, NotEquals
from proveit.numbers import Add, Exp, Integer, Mult, Real, zero

# build up the expression from sub-expressions
expr = Conditional(Equals(Exp(a, b), Mult(Exp(a, c), Exp(a, d))), And(InSet(a, Real), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer), NotEquals(a, zero), Equals(b, Add(c, d))))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{a^{b} = \left(a^{c} \cdot a^{d}\right) \textrm{ if } a \in \mathbb{R} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a \neq 0 ,  b = \left(c + d\right)\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 24 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9, 10, 11, 12, 13
6	Operation	operator: 34 operands: 14
7	Operation	operator: 15 operands: 16
8	Operation	operator: 20 operands: 17
9	Operation	operator: 20 operands: 18
10	Operation	operator: 20 operands: 19
11	Operation	operator: 20 operands: 21
12	Operation	operator: 22 operands: 23
13	Operation	operator: 24 operands: 25
14	ExprTuple	38, 31
15	Literal
16	ExprTuple	26, 27
17	ExprTuple	38, 28
18	ExprTuple	31, 29
19	ExprTuple	39, 29
20	Literal
21	ExprTuple	40, 29
22	Literal
23	ExprTuple	38, 30
24	Literal
25	ExprTuple	31, 32
26	Operation	operator: 34 operands: 33
27	Operation	operator: 34 operands: 35
28	Literal
29	Literal
30	Literal
31	Variable
32	Operation	operator: 36 operands: 37
33	ExprTuple	38, 39
34	Literal
35	ExprTuple	38, 40
36	Literal
37	ExprTuple	39, 40
38	Variable
39	Variable
40	Variable

Expression of type Conditional¶

from the theory of proveit.numbers.exponentiation¶

Expression of type Conditional ¶

from the theory of proveit.numbers.exponentiation ¶