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Proof step 12 from proof validrefs-putbyte-field (previous step)

st[r0 -- i '] = refval(r1), validrefs(str, r1 ' + refs, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), 0 < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, 0 ≤ i, is_obj(str, r0, st), ∀ by, fieldvar, class, r, st0, ty, str, refs0. # refs0 < # (r0 + r1 + refs) → ( validrefs(str, refs0, ty, st0[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ r0 -- _length = r -- mkfs(class, byte_type, fieldvar) ', r0 = jvmref, validrefs(str, r0 ' + r1 ' + refs, ty, st), junkref(str, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
st[r -- i '] = refval(r1), is_array(str, r, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs, st[r -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), is_obj(str, r, st), 0 ≤ i, 0 < st[r -- _length] .intval, ∀ by, fieldvar, class, r2, st0, ty, str, refs0. # refs0 < # (r + r1 + refs) → ( validrefs(str, refs0, ty, st0[r2 -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st0) ∨ validrefs(str, refs0, ty, st0)) ⊦ _length = mkfs(class, byte_type, fieldvar) ', r = jvmref, junkref(str, r, st), validrefs(str, r ' + r1 ' + refs, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ int_type ≠ byte_type], [CSIMPFORWARD : ⊦ mkfs(class1, ty, fieldvar) ' = _length → class1 = `*Array*' .class ∧ ty = int_type ∧ fieldvar = `length' .field], [CSIMPSEQ : ⊦ is_obj(str, r, st) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)])]]