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Proof step 31 from proof compatarray-mode (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
st[r -- _type] .type = mkarraytype(ty), is_arraytype(st[r -- _type] .type), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), r ∈ st, 0 ≤ st[r -- _length] .intval ⊦ r = jvmref, (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → compat(str, st[r -- j '], ty, st[_mode, val])) ↔ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], ty, 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)]]