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Proof step 52 from proof junkrefs-put-refval-02 (previous step)

is_array(str, r1, st[r -- i ', refval(r0)]) ∧ (st[r -- i ', refval(r0)][r1 -- _type]) .type ≤ ty, is_array(str, r1, st), acc ≠ [] ∧ (∃ i0. 0 ≤ i0 ∧ i0 < (st[r -- i ', refval(r0)][r1 -- _length]) .intval ∧ is_referencevalue(st[r -- i ', refval(r0)][r1 -- i0 ']) ∧ acc .first = (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval ∧ junkrefs(str, acc, (st[r -- i ', refval(r0)][r1 -- _type]) .type .type, st[r -- i ', refval(r0)])), mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, st[r1 -- _type] .type ≤ ty, ∀ st, r0, r, str, ty, i. mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type ∧ junkrefs(str, acc, ty, st[r -- i ', refval(r0)]) → r = jvmref ∨ r0 = jvmref ∨ junkrefs(str, acc, ty, st) ∨ junkref(str, r0, st) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, junkref(str, r0, st), acc ≠ [] ∧ (∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ acc .first = st[r1 -- i0 '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
acc .first = (st[r -- i ', refval(r0)][r1 -- i0 ']) .refval, mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type, is_array(str, r1, st[r -- i ', refval(r0)]), st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), i0 < st[r1 -- _length] .intval, is_referencevalue(st[r -- i ', refval(r0)][r1 -- i0 ']), junkrefs(str, acc, st[r1 -- _type] .type .type, st[r -- i ', refval(r0)]), 0 ≤ i0, 0 < st[r1 -- _length] .intval, ∀ st, r0, r, str, ty, i. mkarraytype(st[r0 -- _type] .type) ≤ st[r -- _type] .type ∧ junkrefs(str, acc, ty, st[r -- i ', refval(r0)]) → r = jvmref ∨ r0 = jvmref ∨ junkrefs(str, acc, ty, st) ∨ junkref(str, r0, st) ⊦ r1 = jvmref, r0 = jvmref, r = jvmref, acc = [], junkref(str, r0, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r1 -- i0 ']) ∧ acc .first = st[r1 -- i0 '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st)

Rule argument

[emptyarg]

Additional information

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