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Proof step 58 from proof validrefs-put-array-badindex (previous step)

is_array(str, r0, st[r -- i ', val]) ∧ (st[r -- i ', val][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < 0, 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)) ⊦ refs0 = [] ∨ (∃ i0. 0 ≤ i0 ∧ i0 < (st[r -- i ', val][r0 -- _length]) .intval ∧ is_referencevalue(st[r -- i ', val][r0 -- i0 ']) ∧ refs0 .first = (st[r -- i ', val][r0 -- i0 ']) .refval ∧ validrefs(str, refs0, (st[r -- i ', val][r0 -- _type]) .type .type, 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 57:
is_array(str, r0, st), i < 0, is_array(str, r0, st[r -- i ', val]), 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)) ⊦ r0 = jvmref, refs0 = [] ∨ (∃ i0. 0 ≤ i0 ∧ i0 < st[r0 -- _length] .intval ∧ is_referencevalue(st[r -- i ', val][r0 -- i0 ']) ∧ refs0 .first = (st[r -- i ', val][r0 -- i0 ']) .refval ∧ validrefs(str, refs0, st[r0 -- _type] .type .type, st[r -- i ', val])) ↔ validrefs(str, r0 ' + refs0, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , is_valid_ref-isarray, ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)], [CSIMPNAMEDSEQ : javastore, , type-at, ⊦ (st[r -- i ', val] [r0 -- _type ] ) = st[r0 -- _type]], [CSIMPNAMEDSEQ : javastore, , length-at, ⊦ (st[r -- i ', val] [r0 -- _length ] ) = st[r0 -- _length]])]]