Expression of type Forall

from the theory of proveit.logic.booleans

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 A, P, PofA, Q, QofA
from proveit.logic import Boolean, Forall, Implies, QimplPofFalse, QimplPofTrue

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [P, Q], instance_expr = Forall(instance_param_or_params = [A], instance_expr = Implies(QofA, PofA), domain = Boolean), conditions = [QimplPofTrue, QimplPofFalse])

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_{P, Q~|~Q\left(\top\right) \Rightarrow P\left(\top\right), Q\left(\bot\right) \Rightarrow P\left(\bot\right)}~\left[\forall_{A \in \mathbb{B}}~\left(Q\left(A\right) \Rightarrow P\left(A\right)\right)\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: 7 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	35, 34
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 37 body: 14
12	Operation	operator: 23 operands: 15
13	Operation	operator: 23 operands: 16
14	Conditional	value: 17 condition: 18
15	ExprTuple	19, 20
16	ExprTuple	21, 22
17	Operation	operator: 23 operands: 24
18	Operation	operator: 25 operands: 26
19	Operation	operator: 34 operand: 32
20	Operation	operator: 35 operand: 32
21	Operation	operator: 34 operand: 33
22	Operation	operator: 35 operand: 33
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	37, 31
27	ExprTuple	32
28	ExprTuple	33
29	Operation	operator: 34 operand: 37
30	Operation	operator: 35 operand: 37
31	Literal
32	Literal
33	Literal
34	Variable
35	Variable
36	ExprTuple	37
37	Variable