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Proof step 39 from proof validrefs-putbyte-field (previous step)

is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, refs1 = [] ∨ 0 ≤ i ∧ i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval ∧ is_referencevalue(st[r0 -- i ']) ∧ refs1 .first = st[r0 -- i '] .refval ∧ validrefs(str, refs1, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), ∀ by, fieldvar, class, r, st, ty, str, refs0. # refs0 < # (r0 + refs1) → ( validrefs(str, refs0, ty, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st) ∨ validrefs(str, refs0, ty, st)) ⊦ refs1 = [], r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
refs1 .first = st[r0 -- i '] .refval, is_array(str, r0, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), st[r0 -- _type] .type ≤ ty, i < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), validrefs(str, refs1, st[r0 -- _type] .type .type, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]), 0 ≤ i, 0 < (st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)][r0 -- _length]) .intval, ∀ by, fieldvar, class, r, st, ty, str, refs0. # refs0 < # (r0 + refs1) → ( validrefs(str, refs0, ty, st[r -- mkfs(class, byte_type, fieldvar) ', byteval(by)]) → refs0 = [] ∨ junkref(str, refs0 .first, st) ∨ validrefs(str, refs0, ty, st)) ⊦ refs1 = [], r0 = jvmref, junkref(str, r0, st), validrefs(str, r0 ' + refs1, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j])]]