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Proof step 22 from proof validrefs-putshort-field (previous step)

validrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st), st[r0 -- i '] = refval(r1), i < (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- _length]) .intval, is_array(str, r0, st), 0 < (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- _length]) .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), validrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + r1 + refs0) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref, ¬ st[r0 -- _length] .intval ≤ i ∧ validrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st), ¬ st[r0 -- _length] .intval ≤ i ∧ r1 ≠ jvmref ∧ (¬ st[r1 -- _type] .type ≤ st[r0 -- _type] .type .type ∨ junkref(str, r1, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
st[r0 -- i '] = refval(r1), validrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st), i < (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- _length]) .intval, is_array(str, r0, st), 0 < (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- _length]) .intval, 0 ≤ i, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']), validrefs(str, r1 ' + refs0, st[r0 -- _type] .type .type, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]), st[r0 -- _length] .intval ≤ i, st[r0 -- _length] .intval < (st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)][r0 -- _length]) .intval, ∀ sho, fieldvar, class, r, st, ty, str, refs. # refs < # (r0 + r1 + refs0) → ( validrefs(str, refs, ty, st[r -- mkfs(class, short_type, fieldvar) ', shortval(sho)]) ∧ is_shortvalue(st[r -- mkfs(class, short_type, fieldvar) ']) → refs = [] ∨ junkref(str, refs .first, st) ∨ validrefs(str, refs, ty, st)) ⊦ r0 = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0])]]