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Proof step 32 from proof validrefs-putbar-01 (previous step)

st[r0 -- i0 '] = refval(r1), 0 ≤ i0, 0 < st[r0 -- _length] .intval, is_array(str, r0, st), okbytearray(r, st), is_array(str, r0, putByteArray(bytes, r, i, st)), st[r0 -- _type] .type ≤ ty, i0 < st[r0 -- _length] .intval, validrefs(str, r1 ' + refs1, st[r0 -- _type] .type .type, putByteArray(bytes, r, i, st)), ∀ i, bytes, ty, r2, str, st0, r, refs. # refs < # (r1 + refs1) → ( okbytearray(r, st0) ∧ validrefs(str, r2 ' + refs, ty, putByteArray(bytes, r, i, st0)) → junkref(str, r2, st0) ∨ validrefs(str, r2 ' + refs, ty, st0)) ⊦ r0 = r, r0 = jvmref, junkref(str, r0, st), validrefs(str, r1 ' + refs1, st[r0 -- _type] .type .type, st)

User applied rule apply induction

And obtained the following new goals

Proof step 31:
junkref(str, r1, st) ∨ validrefs(str, r1 ' + refs1, st[r0 -- _type] .type .type, st), st[r0 -- i0 '] = refval(r1), 0 ≤ i0, 0 < st[r0 -- _length] .intval, is_array(str, r0, st), okbytearray(r, st), is_array(str, r0, putByteArray(bytes, r, i, st)), st[r0 -- _type] .type ≤ ty, i0 < st[r0 -- _length] .intval, validrefs(str, r1 ' + refs1, st[r0 -- _type] .type .type, putByteArray(bytes, r, i, st)), ∀ i, bytes, ty, r2, str, st0, r, refs. # refs < # (r1 + refs1) → ( okbytearray(r, st0) ∧ validrefs(str, r2 ' + refs, ty, putByteArray(bytes, r, i, st0)) → junkref(str, r2, st0) ∨ validrefs(str, r2 ' + refs, ty, st0)) ⊦ r0 = r, r0 = jvmref, junkref(str, r0, st), validrefs(str, r1 ' + refs1, st[r0 -- _type] .type .type, st)

Rule argument

[substlist-arg: [i, bytes, ty, r2, str, st0, r, refs] → [i, bytes, st[r0 -- _type] .type .type, r1, str, st, r, refs1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (i, bytes, st[r0 -- _type] .type .type, r1, str, st, r, refs1)]]