def lt_m
bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix32.bend:287
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fix32.bend as Fix32
import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW
287def lt_m(+mp: Nat, +hp: {C.pow2(32n) == 1n+mp : Nat}, +x: U32) -> {Nat.is_lt(SG.u32_val(x), 1n+mp) == True{} : Bool}:
288 Equal.trans(Bool, Nat.is_lt(SG.u32_val(x), 1n+mp), Nat.is_lt(SG.u32_val(x), C.pow2(32n)), True{}, Equal.cong(Nat, Bool, t => Nat.is_lt(SG.u32_val(x), t), 1n+mp, C.pow2(32n), Equal.sym(Nat, C.pow2(32n), 1n+mp, hp)), WW.lt_of_fits(32n, SG.u32_val(x), LW.vb(x)))