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Proof step 51 from proof putarray-addarray-override (previous step)

r ≠ r0 ∨ r = r0 ∧ is_fskey(_length) ∧ _length ≠ _length ∧ _length ≠ _type ∨ r = r0 ∧ is_indexkey(_length) ∧ (_length .index < 0 ∨ n→i(# vals0) ≤ _length .index), fs ' = _length, i + n→i(# vals) ≤ n→i(# vals0), 0 ≤ i ⊦ r0 -- _length ∈ st ↔ r0 -- _length ∈ addarray(r, ty, firstn(i→n(i), vals0) + vals + restn(i→n(i) + # vals, vals0), st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
⊦ rk ∈ st → rk ∈ addarray(r, ty, vals, st)
Proof step 47:
⊦ r ≠ r0 → (r -- sk ∈ addarray(r0, ty, vals, st) ↔ r -- sk ∈ st)
Proof step 48:
⊦ r ∈ addarray(r, ty0, vals, st)
Proof step 49:
⊦ r -- _length ∈ addarray(r, ty, vals, st)
Proof step 50:
fs ' = _length, is_indexkey(_length), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), _length .index < 0 ∨ n→i(# vals0) ≤ _length .index ⊦ r0 -- _length ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ is_fskey(_length)])]]