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Expression of type Forall

from the theory of proveit.numbers.multiplication

In [1]:
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 a, b, k
from proveit.logic import Equals, Forall, NotEquals
from proveit.numbers import Complex, Exp, Mult, zero
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = Equals(Exp(Exp(a, b), k), Exp(a, Mult(b, k))), domain = Complex, condition = NotEquals(a, zero))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{a, b \in \mathbb{C}~|~a \neq 0}~\left((a^{b})^{k} = a^{b \cdot k}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 28
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operands: 8
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11, 12
9Literal
10ExprTuple13, 14, 15
11Operationoperator: 27
operands: 16
12Operationoperator: 27
operands: 17
13Operationoperator: 19
operands: 18
14Operationoperator: 19
operands: 20
15Operationoperator: 21
operands: 22
16ExprTuple23, 33
17ExprTuple31, 24
18ExprTuple31, 25
19Literal
20ExprTuple32, 25
21Literal
22ExprTuple31, 26
23Operationoperator: 27
operands: 28
24Operationoperator: 29
operands: 30
25Literal
26Literal
27Literal
28ExprTuple31, 32
29Literal
30ExprTuple32, 33
31Variable
32Variable
33Variable