def c2_eq

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/f64sqr.bend:138

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

138def c2_eq(+S2: Nat) -> {Nat.sub(Nat.sub(Nat.add(2n+S2, 2n+S2), 1n), 2n) == 1n+Nat.add(S2, S2) : Nat}:
139  +e1 = Equal.trans(Nat, Nat.add(S2, 2n+S2), 1n+Nat.add(S2, 1n+S2), 1n+1n+Nat.add(S2, S2), N.add_succ(S2, 1n+S2), Equal.cong(Nat, Nat, z => 1n+z, Nat.add(S2, 1n+S2), 1n+Nat.add(S2, S2), N.add_succ(S2, S2)))
140  Equal.cong(Nat, Nat, z => Nat.sub(z, 1n), Nat.add(S2, 2n+S2), 1n+1n+Nat.add(S2, S2), e1)