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Proof step 14 from proof compatarray-isarray-01 (previous step)

is_array(r, st), r -- _length ∈ st, is_arraytype(st[r -- _type] .type), r ∈ st, ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], st[r -- _type] .type .type, st) ⊦ (0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], st[r -- _type] .type .type, st)) ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ is_integervalue(st[r -- _length])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
st[r -- _type] .type = mkarraytype(ty), is_array(r, st), r -- _length ∈ st, is_arraytype(st[r -- _type] .type), r ∈ st, ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], ty, st) ⊦ (0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], ty, st)) ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ is_integervalue(st[r -- _length])

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)]]