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Proof step 10 from proof pathex-class (previous step)

validrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ⊦ r = (st[r -- fs '] .refval ' + refs) .last, st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_valid_ref(str, st[r -- fs '] .refval, st) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type), st[r -- fs '] .refval = jvmref ∧ (st[r -- fs '] .refval ' + refs) .last = jvmref, st[r -- fs '] .refval ≠ jvmref ∧ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ path∃(str, st[r -- fs '] .refval, (st[r -- fs '] .refval ' + refs) .last, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ r = jvmref → (validrefs(str, r ' + refs, ty, st) ↔ refs = [])
Proof step 9:
st[r -- fs '] .refval ≠ jvmref, validrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st), is_referencevalue(st[r -- fs ']), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st) ⊦ r = (st[r -- fs '] .refval ' + refs) .last, st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_valid_ref(str, st[r -- fs '] .refval, st) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type), st[r -- fs '] .refval = jvmref ∧ (st[r -- fs '] .refval ' + refs) .last = jvmref, st[r -- fs '] .refval ≠ jvmref ∧ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ path∃(str, st[r -- fs '] .refval, (st[r -- fs '] .refval ' + refs) .last, st)

Rule argument

[crewrite-arg: validrefs-null , F , [st, ty, refs, r, str] → [st, fs .type, refs, st[r -- fs '] .refval, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRATERMS : (st, fs .type, refs, st[r -- fs '] .refval, str)]]