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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, b
from proveit.logic import Equals, Forall, Implies
In [2]:
# build up the expression from sub-expressions
expr = Forall([a, b, Q], Equals(Conditional(a, Q), Conditional(b, Q)).with_wrapping_at(1), condition = Implies(Q, Equals(a, b)))
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, b, Q~|~Q \Rightarrow \left(a = b\right)}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q\right.. \\  = \left\{b \textrm{ if } Q\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
4ExprTuple17, 18, 14
5Conditionalvalue: 6
condition: 7
6Operationoperator: 15
operands: 8
7Operationoperator: 9
operands: 10
8ExprTuple11, 12
9Literal
10ExprTuple14, 13
11Conditionalvalue: 17
condition: 14
12Conditionalvalue: 18
condition: 14
13Operationoperator: 15
operands: 16
14Variable
15Literal
16ExprTuple17, 18
17Variable
18Variable