| ∀ n, buf. is-encoded(nx0 + n ', buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded(nx0, buf0) ∧ is-encoded(rnode(n), buf1)) ⊦ (∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded(rnode(m), buf0) ∧ is-encoded(nx0 + n ', buf1)) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ (∃ buf2, buf1. buf0 = buf2 + buf1 ∧ is-encoded(rnode(m), buf2) ∧ is-encoded(nx0, buf1)) ∧ is-encoded(rnode(n), buf1)) |
∀ n, buf. is-encoded(nx0 + n ', buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded(nx0, buf0) ∧ is-encoded(rnode(n), buf1)), ∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded(rnode(m), buf0) ∧ is-encoded(nx0 + n ', buf1) ⊦ ∃ buf0, buf1. buf = buf0 + buf1 ∧ (∃ buf2, buf1. buf0 = buf2 + buf1 ∧ is-encoded(rnode(m), buf2) ∧ is-encoded(nx0, buf1)) ∧ is-encoded(rnode(n), buf1)
∀ n, buf. is-encoded(nx0 + n ', buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded(nx0, buf0) ∧ is-encoded(rnode(n), buf1)), ∃ buf0, buf1. buf = buf0 + buf1 ∧ (∃ buf2, buf1. buf0 = buf2 + buf1 ∧ is-encoded(rnode(m), buf2) ∧ is-encoded(nx0, buf1)) ∧ is-encoded(rnode(n), buf1) ⊦ ∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded(rnode(m), buf0) ∧ is-encoded(nx0 + n ', buf1)