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Proof step 27 from proof pathex-put-cyclic (previous step)

st[r0 -- _type] .type = mkclasstype(class0), validrefs(str, (r ' + refs0) + r0 ', st[r -- _type] .type, st), st[r -- _type] .type ≤ ty, mkfs(class, ty, fieldvar) ' ∈ instfields(class0), r0 = jvmref ∨ r0 ≠ jvmref ∧ is_valid_ref(str, r0, st) ∧ st[r0 -- _type] .type ≤ mkclasstype(class0) ⊦ _type = mkfs(class, ty, fieldvar) ', r = r0, r0 = jvmref, r = jvmref, validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), r ∈ refs0, dups(refs0), r0 ∈ refs0, is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[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 26:
st[r0 -- _type] .type = mkclasstype(class0), is_valid_ref(str, r0, st), 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, _type = mkfs(class, ty, fieldvar) ', is_obj(str, r0, st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), r0 ∈ refs0, dups(refs0), r ∈ refs0, validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, ty, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ class ≤ class], [CSIMPSEQ : ⊦ mkclasstype(class1) ≤ mkclasstype(class2) ↔ class1 ≤ class2])]]