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Proof step 42 from proof validrefs-put-notin-02 (previous step)

is_array(str, r1, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- _type]) .type ≤ ty, acc + r0 ' = r2 ' + refs, st[r1 -- i '] = refval(r2), is_array(str, r1, st), okval(val, ty0), st[r1 -- _type] .type ≤ ty, i < st[r1 -- _length] .intval, validrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), 0 ≤ i, 0 < st[r1 -- _length] .intval, ∀ 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, acc + r0 ' = [] ∨ (∃ i. 0 ≤ i ∧ i < (st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- _length]) .intval ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- i ']) ∧ (acc + r0 ') .first = (st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- i ']) .refval ∧ validrefs(str, acc + r0 ', (st[r -- mkfs(class, ty0, fieldvar) ', val][r1 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val])), r0 ≠ r2 ∧ ¬ r0 ∈ refs, ¬ r2 ∈ acc ∧ r2 ≠ r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
st[r1 -- i '] = refval(r2), acc + r0 ' = r2 ' + refs, 0 < st[r1 -- _length] .intval, 0 ≤ i, validrefs(str, r2 ' + refs, st[r1 -- _type] .type .type, st), i < st[r1 -- _length] .intval, st[r1 -- _type] .type ≤ ty, okval(val, ty0), is_array(str, r1, st), ∀ 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 ⊦ mkfs(class, ty0, fieldvar) ' = _length, mkfs(class, ty0, fieldvar) ' = _type, r = r1, r1 = jvmref, r ∈ acc, ¬ r2 ∈ acc ∧ r2 ≠ r0, r0 ≠ r2 ∧ ¬ r0 ∈ refs, ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ r2 = st[r1 -- i0 '] .refval ∧ validrefs(str, st[r1 -- i0 '] .refval ' + refs, st[r1 -- _type] .type .type, st[r -- mkfs(class, ty0, fieldvar) ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ fs ' ≠ _length ∧ fs ' ≠ _type → ( is_array (str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ refs + r ' ≠ []])]]