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
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, Forall, TRUE

In [2]:
# build up the expression from sub-expressions
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))

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, 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)

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
4ExprTuple11, 17, 18
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Conditionalvalue: 11
condition: 10
9Conditionalvalue: 11
condition: 12
10Operationoperator: 14
operands: 13
11Variable
12Operationoperator: 14
operands: 15
13ExprTuple17, 16, 18
14Literal
15ExprTuple17, 18
16Literal
17ExprRangelambda_map: 19
start_index: 22
end_index: 20
18ExprRangelambda_map: 21
start_index: 22
end_index: 23
19Lambdaparameter: 29
body: 24
20Variable
21Lambdaparameter: 29
body: 25
22Literal
23Variable
24IndexedVarvariable: 26
index: 29
25IndexedVarvariable: 27
index: 29
26Variable
27Variable
28ExprTuple29
29Variable