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Expression of type Forall

from the theory of proveit.numbers.addition.subtraction

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, c
from proveit.logic import Equals, Forall
from proveit.numbers import Add, Complex, Neg
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, c], instance_expr = Equals(Add(c, a, Neg(b)), c), domain = Complex, condition = Equals(a, b))
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, c \in \mathbb{C}~|~a = b}~\left(\left(c + a - b\right) = c\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
4ExprTuple27, 30, 25
5Conditionalvalue: 6
condition: 7
6Operationoperator: 22
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 25
9Literal
10ExprTuple12, 13, 14, 15
11Operationoperator: 16
operands: 17
12Operationoperator: 20
operands: 18
13Operationoperator: 20
operands: 19
14Operationoperator: 20
operands: 21
15Operationoperator: 22
operands: 23
16Literal
17ExprTuple25, 27, 24
18ExprTuple27, 26
19ExprTuple30, 26
20Literal
21ExprTuple25, 26
22Literal
23ExprTuple27, 30
24Operationoperator: 28
operand: 30
25Variable
26Literal
27Variable
28Literal
29ExprTuple30
30Variable