# from the theory of proveit.core_expr_types.operations¶

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.
# import Expression classes needed to build the expression
from proveit import f, n
from proveit.core_expr_types import f__x_1_to_n, f__y_1_to_n, x_1_to_n, y_1_to_n
from proveit.logic import Equals, Forall
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [f, x_1_to_n, y_1_to_n], instance_expr = Equals(f__x_1_to_n, f__y_1_to_n).with_wrapping_at(2), condition = Equals([x_1_to_n], [y_1_to_n])), domain = Natural)

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_{n \in \mathbb{N}}~\left[\forall_{f, x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}~|~\left(x_{1}, x_{2}, \ldots, x_{n}\right) = \left(y_{1}, y_{2}, \ldots, y_{n}\right)}~\left(\begin{array}{c} \begin{array}{l} f\left(x_{1}, x_{2}, \ldots, x_{n}\right) =  \\ f\left(y_{1}, y_{2}, \ldots, y_{n}\right) \end{array} \end{array}\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: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 30
body: 4
3ExprTuple30
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 11
6Operationoperator: 9
operands: 10
7Literal
8ExprTuple11
9Literal
10ExprTuple30, 12
11Lambdaparameters: 13
body: 14
12Literal
13ExprTuple23, 25, 26
14Conditionalvalue: 15
condition: 16
15Operationoperator: 18
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 21
18Literal
19ExprTuple22, 24
20Operationoperator: 23
operands: 22
21Operationoperator: 23
operands: 24
22ExprTuple25
23Variable
24ExprTuple26
25ExprRangelambda_map: 27
start_index: 29
end_index: 30
26ExprRangelambda_map: 28
start_index: 29
end_index: 30
27Lambdaparameter: 36
body: 31
28Lambdaparameter: 36
body: 32
29Literal
30Variable
31IndexedVarvariable: 33
index: 36
32IndexedVarvariable: 34
index: 36
33Variable
34Variable
35ExprTuple36
36Variable