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Expression of type Forall

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.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Q, a
from proveit.logic import Equals, Forall, TRUE
In [2]:
# build up the expression from sub-expressions
expr = Forall([a, Q], Equals(Conditional(a, Q), Conditional(a, Equals(Q, TRUE))).with_wrapping_at(1))
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_{a, Q}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q\right.. \\  = \left\{a \textrm{ if } Q = \top\right.. \end{array} \end{array}\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: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple9, 13
5Operationoperator: 11
operands: 6
6ExprTuple7, 8
7Conditionalvalue: 9
condition: 13
8Conditionalvalue: 9
condition: 10
9Variable
10Operationoperator: 11
operands: 12
11Literal
12ExprTuple13, 14
13Variable
14Literal