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Theorem eq-write-2-h

⊦ nz ≠ nz0 → ( (cu[nx, ny, nz := a0])[nx0, ny0, nz0 := a1] = (cu[nx0, ny0, nz0 := b1])[nx, ny, nz := b0] ↔ (nx < #x cu ∧ ny < #y cu ∧ nz < #z cu → a0 = b0) ∧ (nx0 < #x cu ∧ ny0 < #y cu ∧ nz0 < #z cu → a1 = b1))

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