This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem repsconst

Description: Construct a function mapping a half-open range of nonnegative integers to a constant, see also fconstmpt . (Contributed by AV, 4-Nov-2018)

		Ref	Expression
	Assertion	repsconst	$⊢ (S \in V \land N \in ℕ_{0}) \to S repeatS N = (0 ..^N) \times \{S\}$

Proof

Step	Hyp	Ref	Expression
1		reps	$⊢ (S \in V \land N \in ℕ_{0}) \to S repeatS N = (x \in (0 ..^N) ⟼ S)$
2		fconstmpt	$⊢ (0 ..^N) \times \{S\} = (x \in (0 ..^N) ⟼ S)$
3	1 2	eqtr4di	$⊢ (S \in V \land N \in ℕ_{0}) \to S repeatS N = (0 ..^N) \times \{S\}$