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Proof step 57 from proof ex-fits-validrefs-stronger (previous step)

is_array(str, r, st), st[r -- _type] .type = mkarraytype(ty), st[r -- i '] = refval(r0), # refs = # sks0, is_array(str, r, st), fits(r0, sks0, st), validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), i < st[r -- _length] .intval, 0 < st[r -- _length] .intval, 0 ≤ i, ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1] ⊦ r = jvmref, junkref(str, r0, 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)), validrefs(str, r0 ' + refs, ty, st), st[r0 -- _type] .type ≤ ty

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
# refs = # sks0, st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(ty), 0 ≤ i, 0 < st[r -- _length] .intval, i < st[r -- _length] .intval, validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st), fits(r0, sks0, st), is_array(str, r, st), ∀ sks1. sks1 ⊑ sks0 ∧ sks1 ≠ [] → st[r0 -- sks1] .refval = (r0 ' + refs)[# sks1] ⊦ r = jvmref, st[r0 -- _type] .type ≤ ty, validrefs(str, r0 ' + refs, ty, st), junkref(str, r0, 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 ≤ ty ∨ junkref(str, st[r -- i0 '] .refval, st))

Rule argument

[emptyarg]

Additional information

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