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Proof step 38 from proof validrefs-put-badarrayfield-01 (previous step)

is_array(str, r, st), st[r -- _type] .type = mkarraytype(ty0), st[r -- i '] = refval(r1), 0 ≤ i, 0 < st[r -- _length] .intval, junkref(str, r1, st), is_arraytype(st[r0 -- _type] .type), is_array(str, r, st), mkarraytype(ty0) ≤ ty, i < st[r -- _length] .intval, validrefs(str, r1 ' + refs, ty0, st) ⊦ fs ' = _type, fs ' = _length, r = jvmref, junkref(str, r, st[r0 -- fs ', val]), ∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st)), dups((r1 ' + refs) .butlast), r ∈ (r1 ' + refs) .butlast, validrefs(str, r1 ' + refs, ty0, st[r0 -- fs ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
st[r -- i '] = refval(r1), st[r -- _type] .type = mkarraytype(ty0), validrefs(str, r1 ' + refs, ty0, st), i < st[r -- _length] .intval, mkarraytype(ty0) ≤ ty, is_array(str, r, st), is_arraytype(st[r0 -- _type] .type), junkref(str, r1, st), 0 < st[r -- _length] .intval, 0 ≤ i ⊦ r = jvmref, fs ' = _length, fs ' = _type, validrefs(str, r1 ' + refs, ty0, st[r0 -- fs ', val]), r ∈ (r1 ' + refs) .butlast, dups((r1 ' + refs) .butlast), junkref(str, r, st[r0 -- fs ', val]), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ ty0 ∨ junkref(str, st[r -- i0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]