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Proof step 32 from proof compatarray-mode (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
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))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j])]]