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Proof step 60 from proof validrefs-put-badarrayfield-01 (previous step)

¬ (r ≠ jvmref ∧ ¬ is_valid_ref(str, r, st[r0 -- fs ', val])), is_arraytype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st), ∀ st, r0, str, ty, fs, val. is_arraytype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st) → fs ' = _type ∨ fs ' = _length ∨ acc = [] ∨ junkref(str, acc .first, st) ∨ dups(acc .butlast) ∨ validrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ junkref(str, r, st[r0 -- fs ', val]), fs ' = _type, fs ' = _length, junkref(str, r, st), dups((r ' + acc) .butlast), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 59:
is_arraytype(st[r0 -- _type] .type), validrefs(str, r ' + acc, ty, st), is_valid_ref(str, r, st[r0 -- fs ', val]), ∀ st, r0, str, ty, fs, val. is_arraytype(st[r0 -- _type] .type) ∧ validrefs(str, acc, ty, st) → fs ' = _type ∨ fs ' = _length ∨ acc = [] ∨ junkref(str, acc .first, st) ∨ dups(acc .butlast) ∨ validrefs(str, acc, ty, st[r0 -- fs ', val]) ⊦ fs ' = _type, fs ' = _length, r = jvmref, junkref(str, r, st[r0 -- fs ', val]), junkref(str, r, st), dups((r ' + acc) .butlast), validrefs(str, r ' + acc, ty, st[r0 -- fs ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]