Expression of type Forall

from the theory of proveit.core_expr_types.conditionals

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

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, b, Q], instance_expr = Equals(Conditional(a, Q), Conditional(b, Q)).with_wrapping_at(1), condition = Implies(Q, Equals(a, b)))

expr:

# 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

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameters: 4 body: 5
4	ExprTuple	17, 18, 14
5	Conditional	value: 6 condition: 7
6	Operation	operator: 15 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	14, 13
11	Conditional	value: 17 condition: 14
12	Conditional	value: 18 condition: 14
13	Operation	operator: 15 operands: 16
14	Variable
15	Literal
16	ExprTuple	17, 18
17	Variable
18	Variable