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Proof step 34 from proof validrefs-put-badclassfield-01 (previous step)

st[r0 -- _type] .type = mkclasstype(class), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, validrefs(str, r ' + acc, ty, st), is_classtype(st[r -- _type] .type), is_obj(str, r, st), ∀ st, r0, str, ty, fs, val. is_classtype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st) → fs ' = _type ∨ acc = [] ∨ junkref(str, acc .first, st) ∨ fs ' ∈ instfields(st[r0 -- _type] .type .class) ∨ dups(acc .butlast) ∨ validrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), dups((r ' + acc) .butlast), fs ' ∈ instfields(class), junkref(str, r, st), junkref(str, r, st[r0 -- fs ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 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 33:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r0 -- _type] .type = mkclasstype(class), is_obj(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(str, acc, fs .type, st)), is_classtype(st[r -- _type] .type), is_obj(str, r, st), ∀ st, r0, str, ty, fs, val. is_classtype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st) → fs ' = _type ∨ acc = [] ∨ junkref(str, acc .first, st) ∨ fs ' ∈ instfields(st[r0 -- _type] .type .class) ∨ dups(acc .butlast) ∨ validrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ r = jvmref, fs ' = _type, validrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), dups((r ' + acc) .butlast), fs ' ∈ instfields(class), junkref(str, r, st), junkref(str, r, st[r0 -- fs ', val])

Rule argument

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

Additional information

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