# 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 l, m, n
from proveit.core_expr_types import A_1_to_l, B_1_to_m, C_1_to_n
from proveit.logic import And, Forall
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [l, m, n], instance_expr = Forall(instance_param_or_params = [A_1_to_l, B_1_to_m, C_1_to_n], instance_expr = And(A_1_to_l, B_1_to_m, C_1_to_n), condition = And(A_1_to_l, And(B_1_to_m), C_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_{l, m, n \in \mathbb{N}}~\left[\forall_{A_{1}, A_{2}, \ldots, A_{l}, B_{1}, B_{2}, \ldots, B_{m}, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{l}, B_{1} \land  B_{2} \land  \ldots \land  B_{m},C_{1}, C_{2}, \ldots, C_{n}}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{l}\land B_{1} \land  B_{2} \land  \ldots \land  B_{m}\land C_{1} \land  C_{2} \land  \ldots \land  C_{n}\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
2Lambdaparameters: 3
body: 4
3ExprTuple28, 39, 32
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 29
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12, 13
10Lambdaparameters: 22
body: 14
11Operationoperator: 17
operands: 15
12Operationoperator: 17
operands: 16
13Operationoperator: 17
operands: 18
14Conditionalvalue: 19
condition: 20
15ExprTuple28, 21
16ExprTuple39, 21
17Literal
18ExprTuple32, 21
19Operationoperator: 29
operands: 22
20Operationoperator: 29
operands: 23
21Literal
22ExprTuple24, 34, 26
23ExprTuple24, 25, 26
24ExprRangelambda_map: 27
start_index: 38
end_index: 28
25Operationoperator: 29
operands: 30
26ExprRangelambda_map: 31
start_index: 38
end_index: 32
27Lambdaparameter: 44
body: 33
28Variable
29Literal
30ExprTuple34
31Lambdaparameter: 44
body: 35
32Variable
33IndexedVarvariable: 36
index: 44
34ExprRangelambda_map: 37
start_index: 38
end_index: 39
35IndexedVarvariable: 40
index: 44
36Variable
37Lambdaparameter: 44
body: 41
38Literal
39Variable
40Variable
41IndexedVarvariable: 42
index: 44
42Variable
43ExprTuple44
44Variable