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Expression of type Forall

from the theory of proveit.numbers.number_sets.complex_numbers

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
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Conjugate, Mult, i, subtract
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(i, b)
expr = Forall(instance_param_or_params = [a, b], instance_expr = Equals(Conjugate(Add(a, sub_expr1)), subtract(a, sub_expr1)))
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}~\left(\left(\left(a + \left(\mathsf{i} \cdot b\right)\right)^*\right) = \left(a - \left(\mathsf{i} \cdot b\right)\right)\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: 4
body: 5
4ExprTuple19, 24
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 10
operand: 13
9Operationoperator: 15
operands: 12
10Literal
11ExprTuple13
12ExprTuple19, 14
13Operationoperator: 15
operands: 16
14Operationoperator: 17
operand: 20
15Literal
16ExprTuple19, 20
17Literal
18ExprTuple20
19Variable
20Operationoperator: 21
operands: 22
21Literal
22ExprTuple23, 24
23Literal
24Variable