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Proof step 72 from proof validrefs-subset-equiv (previous step)

is_array(str, r, st), st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, r -- i ' ∈ st, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st0), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, st ⊆ st0, is_array(str, r, st), 0 ≤ i, r ∈ st, r -- _length ∈ st, r -- _type ∈ st, junkref(str, r0, st), ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), ∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ (¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, r -- i ' ∈ st, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st0), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, st ⊆ st0, is_array(str, r, st), 0 ≤ i, r ∈ st, r -- _length ∈ st, r -- _type ∈ st, junkref(str, r0, st), ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), ∃ i0. ¬ i0 < 0 ∧ ¬ st[r -- _length] .intval ≤ i0 ∧ is_referencevalue(st[r -- i0 ']) ∧ st[r -- i0 '] .refval ≠ jvmref ∧ (¬ st[st[r -- i0 '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])]]