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Proof step 49 from proof getarray-subset (previous step)

okarray(r, st[r -- _type] .type .type, st0), r ∈ st, n < # getarray(r, st0), st ⊆ st0, okarray(r, st[r -- _type] .type .type, st), is_arraytype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, r -- _length ∈ st, n < i→n(st0[r -- _length] .intval), 0 < st0[r -- _length] .intval, r ∈ st0 ⊦ r = jvmref, noval = st0[r -- n→i(n) '], st0[r -- _length] .intval = 0, getarray(r, st0) = [], r -- n→i(n) ' ∈ st

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 48:
st[r -- _type] .type = mkarraytype(ty), okarray(r, ty, st0), r ∈ st, n < # getarray(r, st0), st ⊆ st0, okarray(r, ty, st), is_arraytype(st[r -- _type] .type), is_typevalue(st[r -- _type]), r -- _type ∈ st, r -- _length ∈ st, n < i→n(st0[r -- _length] .intval), 0 < st0[r -- _length] .intval, r ∈ st0 ⊦ r = jvmref, noval = st0[r -- n→i(n) '], st0[r -- _length] .intval = 0, getarray(r, st0) = [], r -- n→i(n) ' ∈ st

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r -- _type] .type, ty] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r -- _type] .type, ty)]]