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Proof step 17 from proof validrefs-postfix (previous step)

is_obj(str, r, st), validrefs(str, r ' + acc + r0 ' + refs, ty, st), st[r -- _type] .type ≤ ty, ∀ str, refs0, st, ty. ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, acc + refs0, ty, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 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 16:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st), acc + r0 ' + refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (acc + r0 ' + refs) .first = st[r -- fs '] .refval ∧ validrefs(str, acc + r0 ' + refs, fs .type, st)), st[r -- _type] .type ≤ ty, ∀ str, refs0, st, ty. ¬ validrefs(str, refs0, st[refs0 .first -- _type] .type, st) ∧ refs0 ≠ [] → ¬ validrefs(str, acc + refs0, ty, st) ⊦ r = jvmref, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc + r0 ' + refs, r, str)]]