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Proof step 5 from proof in-init-03 (previous step)

∀ r, fs, r0, j, st. r -- fs ' ∈ addarray(r0, vals0, j, st) ∧ r ∈ addarray(r0, vals0, j, st) → r -- fs ' ∈ st, r -- fs ' ∈ addarray(r0, val + vals0, j, st), r ∈ addarray(r0, val + vals0, j, st) ⊦ r -- fs ' ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ addarray(r, val ' + vals, i, st) = (addarray(r, vals, i + 1, st)[r -- i ', val])
Proof step 4:
r -- fs ' ∈ addarray(r0, vals0, j + 1, st), r ∈ (addarray(r0, vals0, j + 1, st)[r0 -- j ', val]), r ∈ addarray(r0, vals0, j + 1, st), ∀ r, fs, r0, j, st. r -- fs ' ∈ addarray(r0, vals0, j, st) ∧ r ∈ addarray(r0, vals0, j, st) → r -- fs ' ∈ st ⊦ r -- fs ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r -- fs ' ∈ st[r0 -- i ', val0] ↔ r -- fs ' ∈ st], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ val + vals = val ' + vals])]]