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Proof step 56 from proof validrefs-putbyte-01 (previous step)

okbytearray(r, st), validrefs(str, r0 ' + refs0, ty, st[r -- i ', byteval(by)]), is_valid_ref(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st[r -- i ', byteval(by)]) → validrefs(str, refs1, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, 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 37:
¬ (is_obj(str, r0, st[r -- i ', byteval(by)]) ∧ (st[r -- i ', byteval(by)][r0 -- _type]) .type ≤ ty), okbytearray(r, st), validrefs(str, r0 ' + refs0, ty, st[r -- i ', byteval(by)]), is_valid_ref(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st[r -- i ', byteval(by)]) → validrefs(str, refs1, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st)
Proof step 55:
is_obj(str, r0, st[r -- i ', byteval(by)]) ∧ (st[r -- i ', byteval(by)][r0 -- _type]) .type ≤ ty, okbytearray(r, st), refs0 = [] ∨ (∃ fs. fs ' ∈ instfields((st[r -- i ', byteval(by)][r0 -- _type]) .type .class) ∧ is_referencevalue(st[r -- i ', byteval(by)][r0 -- fs ']) ∧ refs0 .first = (st[r -- i ', byteval(by)][r0 -- fs ']) .refval ∧ validrefs(str, refs0, fs .type, st[r -- i ', byteval(by)])), is_valid_ref(str, r0, st[r -- i ', byteval(by)]), st[r0 -- _type] .type ≤ ty, ∀ by, i, ty, str, st, r, refs1. # refs1 < # (r0 ' + refs0) → (okbytearray(r, st) ∧ validrefs(str, refs1, ty, st[r -- i ', byteval(by)]) → validrefs(str, refs1, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st[r -- i ', byteval(by)], ty, refs0, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', byteval(by)], ty, refs0, r0, str)]]