def o_case

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/freeze.bend:123

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/src/crypto/curve25519/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/num.bend as M
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/consts.bend as K
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/cong.bend as G

123def o_case(+one: Nat, +h1: {one == 1n : Nat}, +pp: Nat, +hP: {Nat.add(1n+pp, 19n) == WD.sc(255n, one) : Nat}, +x: List<&2, U32>, +cp: List<&2, U32>, +hx: {LM.okb(32n, x, 255n) == True{} : Bool}, +hk: {LM.okb(32n, cp, 128n) == True{} : Bool}, +hv: {K.valo(one, cp) == Nat.add(1n+pp, 38n) : Nat}, +hc: {Nat.is_lt(v(LM.cc(F.carry(F.addl(x, cp), 0))), one) == False{} : Bool}) -> {Nat.add(FS.value(LM.cl(F.carry(F.addl(x, cp), 0))), 1n+pp) == FS.value(x) : Nat}:
124  +P = {1n+pp : Nat}
125  +r = F.carry(F.addl(x, cp), 0)
126  +c = v(LM.cc(r))
127  +vs = FS.value(LM.cl(r))
128  +ev = cs_val(one, h1, pp, x, cp, hx, hk, hv)
129  +ev1 = L.subst(Nat, z => {Nat.add(vs, LM.shn(32n, z)) == Nat.add(FS.value(x), Nat.add(P, 38n)) : Nat}, c, one, o_c(one, h1, pp, hP, x, cp, hx, hk, hv, hc), ev)
130  +ev2 = L.subst(Nat, z => {Nat.add(vs, z) == Nat.add(FS.value(x), Nat.add(P, 38n)) : Nat}, LM.shn(32n, one), Nat.add(Nat.add(P, P), 38n), t_val(one, h1, pp, hP), ev1)
131  +ev3 = Equal.trans(Nat, Nat.add(Nat.add(vs, P), Nat.add(P, 38n)), Nat.add(vs, Nat.add(P, Nat.add(P, 38n))), Nat.add(FS.value(x), Nat.add(P, 38n)), NA.add_assoc(vs, P, Nat.add(P, 38n)), Equal.trans(Nat, Nat.add(vs, Nat.add(P, Nat.add(P, 38n))), Nat.add(vs, Nat.add(Nat.add(P, P), 38n)), Nat.add(FS.value(x), Nat.add(P, 38n)), M.cong_r(vs, Nat.add(P, Nat.add(P, 38n)), Nat.add(Nat.add(P, P), 38n), Equal.sym(Nat, Nat.add(Nat.add(P, P), 38n), Nat.add(P, Nat.add(P, 38n)), NA.add_assoc(P, P, 38n))), ev2))
132  G.cancel_r(Nat.add(vs, P), FS.value(x), Nat.add(P, 38n), ev3)