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Proof step 62 from proof validrefs-put-array-badindex (previous step)

¬ (r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, st[r -- i ', val]) ∨ ¬ (st[r -- i ', val][r0 -- _type]) .type ≤ ty)), i < 0, is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 61:
i < 0, is_valid_ref(str, r0, st), st[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st[r -- i ', val]), ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st), r0 = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]])]]