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Proof step 25 from proof pathex-put-cyclic (previous step)

¬ (is_obj(str, r0, st) ∧ oktype(refval(r), mkfs(class, ty, fieldvar) .type, st) ∧ mkfs(class, ty, fieldvar) ' ≠ _type), 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)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
st[r0 -- _type] .type = mkclasstype(class0), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(class0), is_obj(str, r0, st), validrefs(str, (r ' + refs0) + r0 ', st[r -- _type] .type, st) ⊦ st[r -- _type] .type = void_type, r = r0, r0 = jvmref, r = jvmref, is_reftype(st[r -- _type] .type), validrefs(str, r0 ' + (r ' + refs0) + r0 ', mkclasstype(class0), st[r0 -- mkfs(class, st[r -- _type] .type, fieldvar) ', refval(r)]), r ∈ refs0, dups(refs0), r0 ∈ refs0, is_obj(str, r0, st[r0 -- mkfs(class, st[r -- _type] .type, fieldvar) ', refval(r)]), ∃ refs. dups(refs) ∧ refs .first = r0 ∧ validrefs(str, refs, st[refs .first -- _type] .type, st[refs .first -- mkfs(class, st[r -- _type] .type, fieldvar) ', refval(r)])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ is_obj(str, r, st) → is_valid_ref(str, r, st)], [CSIMPSEQ : ⊦ ty ≠ void_type → mkfs(class, ty, fieldvar) ' ≠ _type], [CSIMPSEQ : ⊦ st[r -- _type] .type = mkclasstype(class) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ oktype(val, ty, st) ↔ okval(val, ty)], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) .type = ty])]]