Algebra.op_left_comm_sym: law of bend-mathlib@0.8.1.0 Import: import bend-mathlib@0.8.1.0/algebra.bend as Algebra Lines 308-317 of bend-mathlib@0.8.1.0/algebra.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/algebra.bend&start_line=308&end_line=317 import Base # Left commutation from associativity and commutativity, reversed to rewrite toward the simple side. law op_left_comm_sym: for ~A: Data for ~op: A -> A -> A for ~assoc: @x: A -> @y: A -> @z: A -> {op(op(x, y), z) == op(x, op(y, z)) : A} for ~comm: @x: A -> @y: A -> {op(x, y) == op(y, x) : A} for +a: A for +b: A for +c: A {op(b, op(a, c)) == op(a, op(b, c)) : A} Uses (2): https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/algebra.bend&name=op_left_comm