# from the theory of proveit.core_expr_types.conditionals¶

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 Conditional, a, m, n
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, Forall, TRUE
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [m, n], instance_expr = Forall(instance_param_or_params = [a, Q_1_to_m, R_1_to_n], instance_expr = Equals(Conditional(a, And(Q_1_to_m, TRUE, R_1_to_n)), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1)), 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_{m, n \in \mathbb{N}}~\left[\forall_{a, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m} ,  \top, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{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
2Lambdaparameters: 3
body: 4
3ExprTuple33, 36
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 27
operands: 9
7Literal
8ExprTuple10
9ExprTuple11, 12
10Lambdaparameters: 13
body: 14
11Operationoperator: 16
operands: 15
12Operationoperator: 16
operands: 17
13ExprTuple24, 30, 31
14Operationoperator: 18
operands: 19
15ExprTuple33, 20
16Literal
17ExprTuple36, 20
18Literal
19ExprTuple21, 22
20Literal
21Conditionalvalue: 24
condition: 23
22Conditionalvalue: 24
condition: 25
23Operationoperator: 27
operands: 26
24Variable
25Operationoperator: 27
operands: 28
26ExprTuple30, 29, 31
27Literal
28ExprTuple30, 31
29Literal
30ExprRangelambda_map: 32
start_index: 35
end_index: 33
31ExprRangelambda_map: 34
start_index: 35
end_index: 36
32Lambdaparameter: 42
body: 37
33Variable
34Lambdaparameter: 42
body: 38
35Literal
36Variable
37IndexedVarvariable: 39
index: 42
38IndexedVarvariable: 40
index: 42
39Variable
40Variable
41ExprTuple42
42Variable