# from the theory of proveit.logic.booleans.conjunction¶

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 B, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Equals, Forall
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall([m], Forall([A_1_to_m, B], Equals(And(A_1_to_m, B), And(And(A_1_to_m), B)).with_wrapping_at(2)), domain = Natural)

Out[2]:
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(expr.latex())

\forall_{m \in \mathbb{N}}~\left[\forall_{A_{1}, \ldots, A_{m}, B}~\left(\begin{array}{c} \begin{array}{l} \left(A_{1} \land \ldots \land A_{m} \land B\right) =  \\ \left(\left(A_{1} \land \ldots \land A_{m}\right) \land B\right) \end{array} \end{array}\right)\right]

In [5]:
expr.style_options()

Out[5]:
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
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
expr.expr_info()

Out[6]:
core typesub-expressionsexpression
0Operationoperator: 6
operand: 2
1ExprTuple2
2Lambdaparameter: 26
body: 3
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operand: 10
5Operationoperator: 8
operands: 9
6Literal
7ExprTuple10
8Literal
9ExprTuple26, 11
10Lambdaparameters: 17
body: 12
11Literal
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Operationoperator: 21
operands: 17
16Operationoperator: 21
operands: 18
17ExprTuple23, 20
18ExprTuple19, 20
19Operationoperator: 21
operands: 22
20Variable
21Literal
22ExprTuple23
23ExprRangelambda_map: 24
start_index: 25
end_index: 26
24Lambdaparameter: 30
body: 27
25Literal
26Variable
27IndexedVarvariable: 28
index: 30
28Variable
29ExprTuple30
30Variable