def c_eq

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqr.bend:134

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N

134# with S0 = 2 + S2 and S1 = 1 + S2: c = 2 S0 - 1 == 1 + 2 S1, S0^2 == c + S1^2, S1^2 == (c - 2) + S2^2
135def c_eq(+S2: Nat) -> {Nat.sub(Nat.add(2n+S2, 2n+S2), 1n) == 1n+Nat.add(1n+S2, 1n+S2) : Nat}:
136  Equal.cong(Nat, Nat, z => 1n+z, Nat.add(S2, 2n+S2), 1n+Nat.add(S2, 1n+S2), N.add_succ(S2, 1n+S2))