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Wiktionary
inconsequently

adv. In an inconsequential way, or a way that suggests a lack of consequence

WordNet
inconsequently

adv. lacking consequence; "`You're so beautifully dressed,' she said and added quite inconsequentially, `Can you stay the night?'" [syn: inconsequentially] [ant: consequentially]

Usage examples of "inconsequently".

In the heart of her desperate confusion and solitude Tossa remembered inconsequently that Czechoslovakia had no coastline, and laughed, genuinely laughed, but no one noticed except, perhaps, Ondrejov, who noticed everything, whether he acknowledged it or not.