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Proof step 15 from proof compatarray-isarray-01 (previous step)

is_array(r, st), ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], st[r -- _type] .type .type, st) ⊦ is_arraytype(st[r -- _type] .type) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], st[r -- _type] .type .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
is_array(r, st), r -- _length ∈ st, is_arraytype(st[r -- _type] .type), r ∈ st, ∀ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i → compat(str, st[r -- i '], st[r -- _type] .type .type, st) ⊦ (0 ≤ j ∧ j < st[r -- _length] .intval → compat(str, st[r -- j '], st[r -- _type] .type .type, st)) ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ is_integervalue(st[r -- _length])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ r -- _length ∈ st → ¬ is_array(r, st)], [CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(r, st)], [CSIMPSEQ : ⊦ is_array(r, st) → ¬ st[r -- _length] .intval < 0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]