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, R, a
from proveit.core_expr_types import Q_1_to_m
from proveit.logic import And, Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [a, Q_1_to_m, R], instance_expr = Equals(Conditional(a, And(And(Q_1_to_m), R)), Conditional(a, And(Q_1_to_m, R))).with_wrapping_at(1))

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, Q_{1}, Q_{2}, \ldots, Q_{m}, R}~\left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m} ,  R\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m} ,  R\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	11, 19, 16
5	Operation	operator: 6 operands: 7
6	Literal
7	ExprTuple	8, 9
8	Conditional	value: 11 condition: 10
9	Conditional	value: 11 condition: 12
10	Operation	operator: 17 operands: 13
11	Variable
12	Operation	operator: 17 operands: 14
13	ExprTuple	15, 16
14	ExprTuple	19, 16
15	Operation	operator: 17 operands: 18
16	Variable
17	Literal
18	ExprTuple	19
19	ExprRange	lambda_map: 20 start_index: 21 end_index: 22
20	Lambda	parameter: 26 body: 23
21	Literal
22	Variable
23	IndexedVar	variable: 24 index: 26
24	Variable
25	ExprTuple	26
26	Variable