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Proof step 46 from proof fits-subset (previous step)

r -- _type ∈ st0 ∧ st0 ⊆ st, is_array(str, r, st0), st[r -- sk] = refval(r0), st0 ⊆ st, fits(r0, sks0, st), is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st0[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, ∀ st0, st, r, str. st0 ⊆ st ∧ fits(r, sks0, st) → junkref(str, r, st0) ∨ fits(r, sks0, st0) ⊦ r = jvmref, junkref(str, r, st0), is_referencevalue(st0[r -- sk]) ∧ (is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class)) ∧ (is_arraytype(st0[r -- _type] .type) → ¬ is_fskey(sk) ∧ ¬ sk .index < 0 ∧ ¬ st0[r -- _length] .intval ≤ sk .index) ∧ fits(st0[r -- sk] .refval, sks0, st0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
st[r -- sk] = refval(r0), r -- _type ∈ st0, is_array(str, r, st0), st0 ⊆ st, fits(r0, sks0, st), is_arraytype(st0[r -- _type] .type), is_indexkey(sk), sk .index < st[r -- _length] .intval, r ∈ st0, 0 ≤ sk .index, 0 < st[r -- _length] .intval, ∀ st0, st, r, str. st0 ⊆ st ∧ fits(r, sks0, st) → junkref(str, r, st0) ∨ fits(r, sks0, st0) ⊦ r = jvmref, junkref(str, r, st0), is_referencevalue(st0[r -- sk]) ∧ ¬ st0[r -- _length] .intval ≤ sk .index ∧ fits(st0[r -- sk] .refval, sks0, st0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ is_classtype (st[r -- _type] .type) → ¬ is_array(str, r, st)])]]