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Proof step 64 from proof validrefs-put-badclassfield (previous step)

st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val]), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0) ∧ ¬ junkref(str0, st[r -- i '] .refval, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, r = jvmref, r = r0, dups((st[r -- i '] .refval ' + refs) .butlast), r ∈ (st[r -- i '] .refval ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), validrefs(str, r ' + st[r -- i '] .refval ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 63:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r0 -- _type] .type = mkclasstype(class), st[r -- _type] .type ≤ ty, 0 ≤ i, validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st[r0 -- fs ', val]), is_referencevalue(st[r -- i ']), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0) ∧ ¬ junkref(str0, st[r -- i '] .refval, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, st[r -- i '] .refval ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, r = jvmref, r = r0, dups((st[r -- i '] .refval ' + refs) .butlast), r ∈ (st[r -- i '] .refval ' + refs) .butlast, fs ' ∈ instfields(class), junkref(str, r, st), st[r -- i '] .refval ' + refs = [] ∨ (∃ i0. 0 ≤ i0 ∧ i0 < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i0 ']) ∧ (st[r -- i '] .refval ' + refs) .first = st[r -- i0 '] .refval ∧ validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st))

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, st[r -- i '] .refval ' + refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, ty, st[r -- i '] .refval ' + refs, r, str)]]