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

is_obj(str, r, st), validrefs(str, r ' + acc, ty, st), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, validrefs(str, r ' + acc, ty0, st)

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 16:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_obj(str, r, st), 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)), ty ≤ ty0, st[r -- _type] .type ≤ ty, st[r -- _type] .type ≤ ty0, ∀ ty, ty0, str, st. ty ≤ ty0 ∧ validrefs(str, acc, ty, st) → validrefs(str, acc, ty0, st) ⊦ r = jvmref, validrefs(str, r ' + acc, ty0, st)

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)]]