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Proof step 62 from proof pathex-put-cyclic (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ r ≠ r0 → (path∃(str, r, r0, st) ↔ (∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = r0 ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[r -- _type] .type, st)))
Proof step 18:
¬ r0 ≠ r, st[r -- _type] .type = mkclasstype(class0), path∃(str, r0, r, st), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r0 -- _type] .type ≤ ty ⊦ r0 = jvmref, r = jvmref, ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r0)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r0)])
Proof step 61:
r0 ≠ r, st[r -- _type] .type = mkclasstype(class0), ∃ refs. refs ≠ [] ∧ refs .first = r0 ∧ refs .last = r ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[r0 -- _type] .type, st), mkfs(class, ty, fieldvar) ' ∈ instfields(class0), st[r0 -- _type] .type ≤ ty ⊦ r0 = jvmref, r = jvmref, ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs (str, refs, (st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r0)][refs .first -- _type]) .type, st[refs .first -- mkfs(class, ty, fieldvar) ', refval(r0)])

Rule argument

[crewrite-arg: pathex-def-nodups , F , [st, r0, r, str] → [st, r, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r, r0, str)]]