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Proof step 26 from proof validrefs-putbyte (previous step)

st[r0 -- _type] .type ≤ ty, validrefs(str, r0 ' + refs0, ty, st), okbytearray(r, st), is_obj(str, r0, st), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st[r -- i ', byteval(by)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 25:
is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, st[r0 -- _type] .type ≤ ty, refs0 = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ refs0 .first = st[r0 -- fs '] .refval ∧ validrefs(str, refs0, fs .type, st)), okbytearray(r, st), is_obj(str, r0, st), ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st) → validrefs(str, refs1, ty, st[r -- i ', byteval(by)])) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st[r -- i ', byteval(by)])

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty, refs0, r0, str] ]

Additional information

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