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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
from proveit.logic import Equals, Forall, InSet, Or
from proveit.numbers import Complex, Mult, ZeroSet, zero
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b], instance_expr = InSet(Mult(a, b), ZeroSet), domain = Complex, condition = Or(Equals(a, zero), Equals(b, 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}~|~\left(a = 0\right) \lor \left(b = 0\right)}~\left(\left(a \cdot b\right) \in \left\{0\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: 16
body: 4
4Conditionalvalue: 5
condition: 6
5Operationoperator: 20
operands: 7
6Operationoperator: 8
operands: 9
7ExprTuple10, 11
8Literal
9ExprTuple12, 13, 14
10Operationoperator: 15
operands: 16
11Operationoperator: 17
operand: 32
12Operationoperator: 20
operands: 19
13Operationoperator: 20
operands: 21
14Operationoperator: 22
operands: 23
15Literal
16ExprTuple30, 31
17Literal
18ExprTuple32
19ExprTuple30, 24
20Literal
21ExprTuple31, 24
22Literal
23ExprTuple25, 26
24Literal
25Operationoperator: 28
operands: 27
26Operationoperator: 28
operands: 29
27ExprTuple30, 32
28Literal
29ExprTuple31, 32
30Variable
31Variable
32Literal