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Proof step 49 from proof validrefs-put-notin-02 (previous step)

is_array(str, r1, st), validrefs(str, (r1 ' + acc) + r0 ', ty, st), okval(val, ty0), st[r1 -- _type] .type ≤ ty, ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 48:
is_array(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), acc + r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r1 -- _length] .intval ∧ is_referencevalue(st[r1 -- i ']) ∧ (acc + r0 ') .first = st[r1 -- i '] .refval ∧ validrefs(str, acc + r0 ', st[r1 -- _type] .type .type, st)), okval(val, ty0), st[r1 -- _type] .type ≤ ty, ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val])

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc + r0 ', r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + r0 ', r1, str)]]