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Proof step 64 from proof junkrefs-put-badfield (previous step)

is_array(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r0 -- fs ', val][r -- _length]) .intval ∧ is_referencevalue(st[r0 -- fs ', val][r -- i ']) ∧ acc .first = (st[r0 -- fs ', val][r -- i ']) .refval ∧ junkrefs(str, acc, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val])), st[r -- _type] .type ≤ ty, ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ⊦ r = jvmref, junkrefs(str, r ' + acc, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
acc .first = st[r -- i '] .refval, junkrefs(str, acc, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, is_array(str, r, st[r0 -- fs ', val]), (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st), i < (st[r0 -- fs ', val][r -- _length]) .intval, is_referencevalue(st[r -- i ']), 0 ≤ i, 0 < (st[r0 -- fs ', val][r -- _length]) .intval, ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ⊦ r = jvmref, acc = [], junkrefs(str, r ' + acc, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']])]]