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Proof step 19 from proof validrefs-append (previous step)

acc + r ' = r1 ' + refs, st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r1), is_obj(str, r0, st), validrefs(str, r ' + refs0, ty0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs, ty1, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0, ty, st), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 18:
is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, acc + r ' = r1 ' + refs, st[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r1), is_obj(str, r0, st), validrefs(str, r ' + refs0, ty0, st), st[r0 -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), validrefs(str, r1 ' + refs, ty1, st), ∀ str, r, refs0, ty0, st, ty. validrefs(str, r ' + refs0, ty0, st) ∧ validrefs(str, acc + r ', ty, st) → validrefs(str, acc + r ' + refs0, ty, st) ⊦ r0 = jvmref, acc + r ' + refs0 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ (acc + r ' + refs0) .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc + r ' + refs0, fs .type, st)), r ≠ r1 ∧ ¬ r ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty, acc + r ' + refs0, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, acc + r ' + refs0, r0, str)]]