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Proof step 52 from proof validrefs-put-array-badindex (previous step)

∃ i0. ¬ i0 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r0 -- i0 ']) ∧ r2 = st[r0 -- i0 '] .refval ∧ validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st), 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, r2 ' + refs, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ ∃ i0. 0 ≤ i0 ∧ i0 < st[r0 -- _length] .intval ∧ is_referencevalue(st[r -- i ', val][r0 -- i0 ']) ∧ r2 = (st[r -- i ', val][r0 -- i0 ']) .refval ∧ validrefs(str, (st[r -- i ', val][r0 -- i0 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val]), r0 = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
0 < st[r0 -- _length] .intval, 0 ≤ i0, i0 < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st[r -- i ', val]), i < 0, is_array(str, r0, st), validrefs(str, st[r0 -- i0 '] .refval ' + refs, st[r0 -- _type] .type .type, st), is_referencevalue(st[r0 -- i0 ']), i < st[r0 -- _length] .intval, ∀ i, str0, ty0, st0, r1, val0. ¬ 0 ≤ i → (validrefs(str0, st[r0 -- i0 '] .refval ' + refs, ty0, st0[r1 -- i ', val0]) ↔ validrefs(str0, st[r0 -- i0 '] .refval ' + refs, ty0, st0)) ⊦ r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r -- i ', val][r0 -- i1 ']) ∧ st[r0 -- i0 '] .refval = (st[r -- i ', val][r0 -- i1 ']) .refval ∧ validrefs(str, (st[r -- i ', val][r0 -- i1 ']) .refval ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDFORWARD : oelem, intlista, transitivity, ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPNAMEDSEQ : int-abs, , zero-gels-01, ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPNAMEDFORWARD : int-abs, , forward-lsle, ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPNAMEDFORWARD : int-abs, , forward-le-01, ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPNAMEDFORWARD : int-abs, , forward-lels, ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : int-abs, , lels-01, ⊦ ¬ i ≤ j ↔ j < i])]]