Many locals might have been expected to display some nervousness about this week's announcement that the IRA is to shut up shop, given that many of them have traditionally viewed the organisation as their protector.
But the 21-year-old woman wheeling the pram had no reservations or misgivings. "That was brilliant, brilliant, fantastic," she said, her face lighting up. "I was happy, no problems at all." She pointed to "the love of my life", her four-month-old daughter, Katy, in the pram, saying: "I'm just going now to put money in her trust fund, so it is a better future for her."
Her sentiments were echoed by Tony Burgoyne, a Sinn Fein supporter who is now almost 70. "If it had been up to me it would have happened five or six years ago," he said. "I'm not being flippant when I say this, but I think the easy part has been done. Now it all starts - putting away the arms is the easy part, that's what held Sinn Fein back. They can go forward now and they'll wipe the floor with the rest of them, north and south."
Inside a local café, Sean McNamara, who described himself as republican-minded, was fulsome: "I thought it was absolutely superb, I was overjoyed. I was frustrated that it didn't come sooner."
A fellow customer concurred: "Excellent, it made sense after such a long time in conflict." A rare note of dissent came from an acne-pocked 15-year-old from Andersonstown who sported a baseball cap and Manchester United shirt.
"I think it's a bad thing," he said flatly. "They were sort of keeping the hoods down a bit and controlling the streets, stuff like that, around the areas. But once they're gone the hoods will start going up again." His mates, he indicated, had mixed feelings: some who lived in areas affected by hoods shared his sentiments, although those in less troubled districts "don't really need an IRA there".
Michael Ferguson, a local Sinn Fein representative, said everyone he had spoken to had welcomed the announcement but some were worried about the possibility of bother from loyalists where the two communities lived close together. "I've heard people conveying concerns about interface areas," he admitted. "They want to know who is going to defend the community. Nobody has said the IRA shouldn't have done this, but there are community concerns."
The IRA's commitment to pursue its political objectives through peaceful, democratic means has been rightly welcomed and recognised by the British and Irish governments as an historic turning point in the centuries-old conflict in Ireland and between Ireland and Britain.
The IRA was amenable to a negotiated compromise because it became possible to achieve its goals through democratic means. The British Government is committed to allowing Irish reunification as soon as it becomes the wish of majorities in both Northern Ireland and the Irish Republic. The proportion of Catholics in Northern Ireland is approaching 50 per cent, and though not all aspire to Irish unity, the combination of a dynamic Irish economy and British neutrality allows for plausible predictions for reunification this century.
The resulting adjustment to national sovereignty would produce a new liberal and democratic Irish state that would remain a member of the European Union and be recognised in international law as a sovereign state.
In the meantime, adjustments to sovereignty allow devolution (through the Northern Ireland Legislative Assembly), cross-border bodies (the North-South Ministerial Council) and inter-governmental relations between Britain and Ireland that transcend the borders dividing the two parts of Ireland and the sea dividing Britain and Ireland.
Rosemary, a white-haired woman in her 50s who has 10 grandchildren, hoped the IRA was correct in predicting a united Ireland was on the way. She hoped to see it herself, but would certainly like to think it would happen for her grandchildren: "But it won't happen overnight, we're not that naive in thinking it will."
Originally from the Ballymurphy estate, one of the early flashpoints in the troubles, she lost a teenaged brother, Eamonn McCormick, in 1972. He was a member of the junior IRA who was shot and fatally injured by troops.
She added: "I'm delighted by the announcement, I am happy about it and everybody in my family is delighted. Sinn Fein is doing a great job with all the odds against them.
"My brother was killed and he's in the graveyard, and thank God he didn't die for nothing. My brother died at 17, and my mother and father died with a broken heart, but I'm sure they're happy now that everything is the way it should be."