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Proof step 31 from proof validrefs-put-last (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 30:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, acc + r0 ' = r1 ' + refs, st[r -- mkfs(class, ty0, fieldvar) '] = refval(r1), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), validrefs(str, r1 ' + refs, ty0, st[r0 -- sk, val]), ∀ str, r0, ty, st, sk, val. ¬ validrefs(str, acc + r0 ', ty, st) ∧ ¬ junkref(str, acc .first, st) ∧ acc ≠ [] ∧ ¬ r0 ∈ acc ∧ sk ≠ _type → ¬ validrefs(str, acc + r0 ', ty, st[r0 -- sk, val]) ⊦ sk = _type, r0 = r, r = jvmref, r0 ∈ acc, junkref(str, r, st), acc + r0 ' = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (acc + r0 ') .first = st[r -- fs '] .refval ∧ validrefs(str, acc + r0 ', fs .type, st)), r0 ≠ r1 ∧ ¬ r0 ∈ refs, ¬ r1 ∈ acc ∧ r1 ≠ r0

Rule argument

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

Additional information

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