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Proof step 18 from proof validrefs-putbar-01 (previous step)

refs0 = r1 + refs1, r1 = (putByteArray(bytes, r, i, st)[r -- i0 ']) .refval, is_array(str, r, st), okbytearray(r, st), is_array(str, r, putByteArray(bytes, r, i, st)), st[r -- _type] .type ≤ ty, i0 < st[r -- _length] .intval, is_referencevalue(putByteArray(bytes, r, i, st)[r -- i0 ']), validrefs(str, refs0, st[r -- _type] .type .type, putByteArray(bytes, r, i, st)), 0 ≤ i0, 0 < st[r -- _length] .intval, ∀ i, bytes, ty, r0, str, st, r, refs. # refs < # refs0 → (okbytearray(r, st) ∧ validrefs(str, r0 ' + refs, ty, putByteArray(bytes, r, i, st)) → junkref(str, r0, st) ∨ validrefs(str, r0 ' + refs, ty, st)) ⊦ r = jvmref, refs0 = [], junkref(str, r, st), ∃ i1. ¬ i1 < 0 ∧ ¬ st[r -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i1 ']) ∧ r1 = st[r -- i1 '] .refval ∧ validrefs(str, refs0, st[r -- _type] .type .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
0 ≤ i0, 0 < st[r -- _length] .intval, is_array(str, r, st), okbytearray(r, st), is_array(str, r, putByteArray(bytes, r, i, st)), st[r -- _type] .type ≤ ty, i0 < st[r -- _length] .intval, is_referencevalue(putByteArray(bytes, r, i, st)[r -- i0 ']), validrefs(str, (putByteArray(bytes, r, i, st)[r -- i0 ']) .refval ' + refs1, st[r -- _type] .type .type, putByteArray(bytes, r, i, st)), ∀ i1, bytes0, ty, r0, str, st0, r2, refs. # refs < # ((putByteArray(bytes, r, i, st)[r -- i0 ']) .refval + refs1) → ( okbytearray(r2, st0) ∧ validrefs(str, r0 ' + refs, ty, putByteArray(bytes0, r2, i1, st0)) → junkref(str, r0, st0) ∨ validrefs(str, r0 ' + refs, ty, st0)) ⊦ r = jvmref, junkref(str, r, st), ∃ i1. ¬ i1 < 0 ∧ ¬ st[r -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i1 ']) ∧ (putByteArray(bytes, r, i, st)[r -- i0 ']) .refval = st[r -- i1 '] .refval ∧ validrefs(str, (putByteArray(bytes, r, i, st)[r -- i0 ']) .refval ' + refs1, st[r -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]