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Proof step 53 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r = jvmref, r0 = jvmref, r = r0, r0 ∈ refs0, dups(refs0), r ∈ refs0, dups(r0 ' + r ' + refs0 + r0 ') ∧ (r0 ' + r ' + refs0 + r0 ') .first = r0 ∧ validrefs (str, r0 ' + r ' + refs0 + r0 ', (st[(r0 ' + r ' + refs0 + r0 ') .first -- mkfs(class, ty, fieldvar) ', refval(r)][(r0 ' + r ' + refs0 + r0 ') .first -- _type]) .type, st[(r0 ' + r ' + refs0 + r0 ') .first -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r -- _type] .type ≤ ty, validrefs(str, r ' + refs0 + r0 ', st[r -- _type] .type, st) ⊦ r = jvmref, r0 = jvmref, r = r0, r0 ∈ refs0, dups(refs0), r ∈ refs0, validrefs (str, r0 ' + r ' + refs0 + r0 ', (st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)][r0 -- _type]) .type, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ dups(refs + r ') ↔ r ∈ refs ∨ dups(refs)], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs])]]